# Nor Haniza SarminUniversiti Teknologi Malaysia | UTM · Department of Mathematics

Nor Haniza Sarmin

Ph D (Mathematics)

## About

520

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Introduction

Universiti Teknologi Malaysia (UTM) has long participated in a wide variety of collaborative relationships with universities, other institutions and individuals in many countries. This cooperation has been valuable to the University and provides exposure to new ideas and new perspectives.

Additional affiliations

April 2016 - March 2018

June 2014 - present

## Publications

Publications (520)

Let G be a finite group. The non-commuting graph of G is a simple graph Γ(G) whose vertices are elements of G∖Z(G), where Z(G) is the center of G, and two distinct vertices a and b are joint by an edge if ab≠ba. In this paper, we study the non-commuting graph of the group U6n. The independent number, clique and chromatic numbers of the non-commutin...

A zero divisor graph of a finite ring is defined as a simple graph with its vertices are the zero divisors of the ring, and two distinct vertices are adjacent if and only if their product is equal to the zero element of the ring. In this research, the zero divisor graph is identified for the ring of 2x2 matrices over integers modulo prime. Since th...

Recently, the study of probabilities in ring theory has shown a significant increase in the field of algebra. Many interesting algebraic structures were modeled to find their probabilities in certain finite rings. In this paper, we introduce a new type of probability in finite rings, namely the squared-zero product probability. The aim is to study...

A graph is a mathematical subject that consists of vertices and edges. Many studies have been done on the graphs of algebraic structures, including groups and rings. A zero divisor graph of a finite ring is defined as a graph with all zero divisors of the ring as its vertices, where two vertices are adjacent when the product of the vertices is the...

Sombor index is a newly developed degree-based topological index which involves the degree of the vertex in a simple connected graph. The Sombor index is known as the square root of the sum of the squared degrees of two adjacent vertices in a graph. Meanwhile, the noncommuting graph associated to a group is a graph where its vertices are the non-ce...

In the field of algebra, the application of probability theory in ring theory has been widely studied by various researchers. In this paper, a type of probability in finite rings, namely the zero product probability is determined for some ring of 2x2 matrices with a single nonzero entry. To obtain the zero product probability, the exact order of th...

Let Γ be a simple graph with the set of vertices and edges. The first Zagreb index of a graph is defined as the sum of the degree of each vertex to the power of two. Meanwhile, the zero divisor graph of a ring , denoted by Γ(), is defined as a graph with its vertex set () * contains the nonzero zero divisors in which two distinct vertices and are a...

The study of rings and graphs has been explored extensively by researchers. To gain a more effective understanding on the concepts of the rings and graphs, more researches on graphs of different types of rings are required. This manuscript provides a different study on the concepts of commutative rings and undirected graphs. The non-zero divisor gr...

In 1987, Head [1] proposed a splicing method as a mathematical model for DNA recombination. In this model, two DNA molecules are cut at specific recognition sites, and the prefix of one molecule is combined with the suffix of the other, creating a new string. Splicing operations in the system are represented as splicing rules, formalizing the proce...

In chemistry, the molecular structure can be represented as a graph. Based on the information from the graph, its characterization can be determined by computing the topological index. Topological index is a numerical value that can be computed by using some algorithms and properties of the graph. Meanwhile, the non-commuting graph is a graph, in w...

The zero-divisor graph of a ring is a graph whose vertices are the collection of zero-divisors of the ring, with two distinct vertices, x and y are connected by an edge if and only if xy=0. Meanwhile, a zero-divisor type graph is a compression of the zero-divisor graph by partitioning the vertices. For ring of integers modulo n, the zero-divisor ty...

The induced subgraph of a unit graph with vertex set as the non unit elements of a ring R is a graph obtained by deleting all unit elements of R. In a graph , a subset of the vertex set is called a perfect code if the balls with radius 1 centred on the subset are pairwise disjoint and their unions yield the whole vertex set. In this paper, we dete...

The aim of this paper is to investigate the non-trivial subring perfect codes in a unit graph associated with the Boolean rings. We prove a subring perfect code of size , where , in the unit graphs associated with the finite Boolean rings . Moreover, we give a necessary and sufficient condition for a subring of an infinite Boolean ring to be a perf...

The unit graph associated with a ring is the graph whose vertices are elements of , and two different vertices and are adjacent if and only if where is the set of unit elements of The aim of this paper is to present the perfect codes in induced subgraph of unit graph associated with some commutative rings with unity in which its vertex set is We ch...

In mathematics, mainly in the field of algebra, the study on probability related to groups and rings is a common topic which is widely discussed by many researchers. This study originated from the commutativity degree, which is introduced to find the probability that two elements in a group commute. Many extensions have been done on the commutativi...

Concepts in graph theory are widely applied in various fields, where graphs are used to describe problems in order to give methods of solutions. In DNA computing, the complexity of DNA splicing process has led to the study on graph splicing system. Basically, a graph splicing system is introduced to illustrate three dimensional DNA splicing process...

A graph in group theory is constructed by using any elements of a group as a set of vertices. Some of the properties of a group are used to form the edges of the graph. A finite group can be represented in a graph by its subgroup structure. A subgroup H of a group G is a subset of G , where H itself is a group under the same operation as in G, wher...

Commuting graphs are characterized by vertices that are non-central elements of a group where two vertices are adjacent when they commute. In this paper, the concept of commuting graph is extended by defining the generalized commuting graph. Furthermore, the generalized commuting graph of the dihedral groups, the quasi-dihedral groups and the semi-...

The induced subgraph of a unit graph with vertex set as the idempotent elements of a ring R is a graph which is obtained by deleting all non idempotent elements of R. Let C be a subset of the vertex set in a graph Γ. Then C is called a perfect code if for any x, y ∈ C the union of the closed neighbourhoods of x and y gives the the vertex set and th...

The study of graph theory was introduced and widely researched since many practical problems can be represented by graphs. A non-zero divisor graph is a graph in which its set of vertices is the non-zero elements of the ring and the vertices x and y are adjacent if and only if xy ≠ 0. In this study, we introduced the non-zero divisor graphs of some...

Graph splicing system is a notion originally used to illustrate the one-dimensional string of DNA splicing in the form of a graph. A graph splicing system is associated with a graph splicing scheme where graph splicing rules are defined. A graph splicing rule restricts the possible cuts to occur on the edges of the initial graph(s) in a graph splic...

An independence polynomial is a type of graph polynomial from graph theory that store combinatorial information such as the graph properties or graph invariants. The independence polynomial of a graph contains coefficients that represent the number of independent sets of certain sizes and the degree of the polynomial denotes the independence number...

An extension of a free abelian lattice group by finite group is a torsion free crystallographic group. It expounds its symmetrical properties or known as homological invariants. One of the methods to compute its homological invariants is by determining the polycyclic presentation of the group. These polycyclic presentations are first shown to satis...

The studies on the energy of a graph have been actively studied since 1978 and there have been various types of energy of graphs proposed and studied by mathematicians all over the world. One of the many types of energy being studied is Seidel energy, where it is defined as the summation of the absolute values of the eigenvalues of the Seidel matri...

The study of graph properties has gathered many attentions in the past years. The graph properties that are commonly studied include the chromatic number, the clique number and the domination number of a finite graph. In this study, a type of graph properties, which is the perfect code is studied. The perfect code is originally used in coding theor...

DNA splicing system is initiated by Head to mathematically model a relation between formal language theory and DNA molecules. In DNA splicing systems, DNA molecules are cut and recombined in specific ways with the existence of enzymes, which are also known as endonucleases, to produce further molecules. The resulting molecules are depicted as splic...

Splicing system was introduced by Head in 1987 in order to explore the recombinant behaviour of deoxyribonucleic acid (DNA) strands in the presence of restriction enzymes and ligases. Restriction enzymes cut the DNA strands into a left - pattern and right-pattern while the ligases recombine the left-pattern of the first string with the right-patter...

A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In this article, by focusing on commutative ring $ R $, we introduce a new notion of unity product graph associate...

Let R be a finite ring. The zero divisors of R are defined as two nonzero elements of R, say x and y where xy = 0. Meanwhile, the probability that two random elements in a group commute is called the commutativity degree of the group. Some generalizations of this concept have been done on various groups, but not in rings. In this study, a variant o...

A non-commuting graph of a finite group $G$ is a graph whose vertices are non-central elements of $G$ and two vertices are adjacent if they don't commute in $G$. In this paper, we study the non-commuting graph of the group $U_{6n}$ and explore some of its properties including the independent number, clique and chromatic numbers. Also, the general f...

Head in 1987 was the first person to introduce the concept of splicing system as a theoretical model for DNA based computation using splicing operation. Splicing operation is a method of cutting and recombining DNA molecules under the influence of restriction enzymes such as ligase. Previous researches have proven that splicing systems with finite...

There are various types of matrices associated with graph in the field of graph theory. A graph can be represented in the form of its adjacency matrix or its incidence matrix. These matrices have their own way of representing a complex graph which have many vertices, edges and directions. In this paper, the incidence matrices of the non-normal subg...

A direct product graph is a graph that is formed from the direct product of two different graphs for two groups G and H, labelled as ΓG and ΓH. Suppose x1 and y1 be the elements in ΓG and, x2 and y2 be the elements in ΓH. Then, two vertices (x1, x2) and (y1, y2) are connected if x1 and y1 are connected in ΓG, and x2 and y2 are connected in ΓH . In...

The mathematical modelling of DNA splicing systems is developed from the biological process of recombinant DNA where DNA molecules are cut and reassociated with the presence of a ligase and restriction enzymes. The molecules resulting from the splicing system generate a language which is known as a splicing language using formal language theory. In...

The coprime graph is defined as a graph where two distinct vertices are adjacent if and only if the order of both vertices are coprime. The Szeged index is the summation of the products of the number of vertices which are lying closer to x than y and vice versa. Meanwhile, the Wiener index is the half-sum of the distances for all vertices of the gr...

In biology, DNA splicing system models the recombination behaviours of DNA molecules which require the presence of restriction enzymes. Since it is quite incompetent to describe DNA splicing system in one-dimensional string, hence graph theory is used in describing the complexity of DNA splicing system. Thus by graph splicing system, a type of semi...

The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring have product zero. In this study, the probability is determined for a finite ring R of matrices over integers modulo four. First, the annihilators of R a...

Mathematical modelling of splicing system has been introduced to initiate a linkage between the study of informational macromolecules that includes DNA and formal language theory. The ability to present the nitrogenous base which is a component in a nucleotide of DNA, as a series of alphabet, ignites this interdisciplinary study. Over the years, re...

In DNA computing, a sticker system is a computing mechanism involving the Watson-Crick complementarity of DNA molecules. The sticker system is known as a language generating device based on the sticker operation which is analyzed through the concept of formal language theory. The grammar of a formal language can be described by determining finite s...

The homological functors of a group have its foundation in homotopy theory and algebraic K-theory. The Schur multiplier of a group is one of the homological functors while the Schur multiplier of pairs of groups is a continuation of the Schur multiplier of a group. Meanwhile, a pair of groups is capable if the precise center or epicenter of the pai...

Let G be a graph. G is said to be a zero divisor graph when its vertices, V(G) are all zero divisors of a finite ring R and two vertices are adjacent if and only if the product of the vertices is zero. In this study, the zero divisor graph is first constructed for the finite ring of square matrices over integers modulo two, using its definition and...

A graph is formed by a pair of vertices and edges. It can be related to groups by using the groups’ properties for its vertices and edges. The set of vertices of the graph comprises the elements or sets from the group while the set of edges of the graph is the properties and condition for the graph. A conjugacy class of an element is the set of ele...

A Bieberbach group is defined to be a torsion free crystallographic group which is an extension of a free abelian lattice group by a finite point group. This paper aims to determine a mathematical representation of a Bieberbach group with quaternion point group of order eight. Such mathematical representation is the exterior square. Mathematical me...

A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy−1 is in the subset S. The subset of the Cayley graph is inverse closed and does not include the identity of the group. For a simple finite grap...

Let G be a finite groupand H is a subgroup of G. The subgroup graph of H in G is defined as a directed simple graph with vertex set G and two distinct elements x and y are adjacent if and only if xy∈H. In this paper, the work on subgroup graph is extended by defining a new graph called the non-normal subgroup graph. The subgroup graph is determined...

Topological indices are the numerical values that can be calculated from a graph and it is calculated based on the molecular graph of a chemical compound. It is often used in chemistry to analyse the physical properties of the molecule which can be represented as a graph with a set of vertices and edges. Meanwhile, the non-commuting graph is the gr...

Let R be a finite ring. In this study, the probability that two random elements chosen from a finite ring have product zero is determined for some finite ring of matrices over Zn. Then, the results are used to construct the zero divisor graph which is defined as a graph whose vertices are the nonzero zero divisors of R and two distinct vertices x a...

Research on commutativity degree has been done by many authors since 1965. The commutativity degree is defined as the probability that two randomly selected elements in a group commute. In this research, an extension of the commutativity degree called the probability that an element of a group fixes a set Ω is explored. The group G in our scope is...

In DNA splicing system, DNA molecules are cut and recombined with the presence of restriction enzymes and a ligase. The splicing system is analysed via formal language theory where the molecules resulting from the splicing system generate a language which is called a splicing language. In nature, DNA molecules can be read in two ways; forward and b...

A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties and chemical reactivity. It is calculated from a graph representing a molecule. Meanwhile, the non-commuting graph, \(\Gamma _G\) of G, is defined as a graph of vertex set whose vertices are non-centr...

A dominating set S of a graph is a subset of the vertex set of the graph in which the closed neighborhood of S is the whole vertex set. A domination polynomial of a graph contains coefficients that represent the number of dominating sets in the graph. A domination polynomial is usually being obtained for common types of graphs but not for graphs as...

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional silicon-chips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules in...

Let G be a finite group and S be a subset of G where S does not include the identity of G and is inverse closed. A Cayley graph of a group G with respect to the subset S is a graph where its vertices are the elements of G and two vertices a and b are connected if ab^(−1) is in the subset S. The energy of a Cayley graph is the sum of all absolute va...

In DNA splicing systems, restriction enzymes and ligases cleave and recombine DNA molecules based on the cleavage pattern of the restriction enzymes. The set of molecules resulting from the splicing system depicts a splicing language. In this research, an algorithm for DNA splicing systems is developed using C++ visual programming. The splicing lan...

In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not co...

A domination polynomial is a type of graph polynomial in which its coefficients represent the number of dominating sets in the graph. There are many researches being done on the domination polynomial of some common types of graphs but not yet for graphs associated to finite groups. Two types of graphs associated to finite groups are the conjugate g...

The modelling of splicing systems is simulated by the process of cleaving and recombining DNA molecules with the presence of a ligase and restriction enzymes which are biologically called as endodeoxyribonucleases. The molecules resulting from DNA splicing systems are known as splicing languages. Palindrome is a sequence of strings that reads the s...

Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use...

DNA splicing system is mathematically modelled by the process of recombinant DNA which focuses on the possible reaction of sets of restriction enzymes and a ligase. The restriction enzymes are known as endodeoxyribonucleases that allow DNA molecules to be cut and reassociated. The cutting point of a restriction enzyme is determined by its cleavage...

Sticker system is a computer model which is coded with single and double-stranded molecules of DNA; meanwhile, Watson-Crick automata is the automata counterpart of the sticker system representing the biological properties of DNA. Both are the modelings of DNA molecules in DNA computing which use the feature of Watson-Crick complementarity. Formerly...

Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral gr...

Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertice...

In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a g...

The study on conjugacy class has started since 1968. A conjugacy class is defined as an equivalence class under the equivalence relation of being conjugate. In this research, let be a 3-generator 5-group and the scope of the graphs is a simple undirected graph. This paper focuses on the determination of the conjugacy classes of where the set omega...

DNA computing, or more generally, molecular computing, is a recent development at the interface of computer science and molecular biology. In DNA computing, many computational models have been proposed in the framework of formal language theory and automata such as Watson-Crick grammars and sticker systems. A Watson-Crick grammar is a grammar model...

Assume is a non-abelian group A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of denoted by is the graph of vertex set whose vertices are non-central elements, in which is the center of and two distinct vertices and are joined by an edge if and only if In this paper...

The independence and clique polynomial are two types of graph polynomial that store combinatorial information of a graph. The independence polynomial of a graph is the polynomial in which its coefficients are the number of independent sets in the graph. The independent set of a graph is a set of vertices that are not adjacent. The clique polynomial...

This research focuses on finding the Wiener index and Zagreb index of the conjugacy class graph for the dihedral group.

This research focuses on introducing one type of static Watson-Crick grammars known as static Watson-Crick linear grammars with their computational power.

A Watson-Crick Petri net is a model that enhances a Petri net with the Watson-Crick complementarity feature adapted from DNA molecules. The transitions of a Watson-Crick Petri net are labelled with pairs of symbols, and a firing sequence of transitions of the Watson-Crick Petri net is considered as successful if and only if it produces complete dou...

The energy of a graph of a group G is the sum of all absolute values of the eigenvalues of the adjacency matrix. An adjacency matrix is a square matrix where the rows and columns consist of 0 or 1-entry depending on the adjacency of the vertices of the graph. A conjugacy class graph is a graph whose vertex set is the non-central conjugacy classes o...

An orbit is defined as the partition of an equivalent relation of elements in a group. In order to obtain the orbit, a group action acting on the elements of the groups is considered. In this study, the orbits of some metabelian groups are found using conjugation action. The metabelian groups considered in this study are some nonabelian metabelian...

In this research, G is a finite 3-generator 2-group of order 16, where G can be a graph which is called the orbit graph. The orbit graph is a graph whose vertices are non-central orbits under the group action of G on a set. The two vertices are adjacent when they are conjugated to each other. Based on the definition of the orbit graph and group act...

There are various aspects of combinatorial information that are stored in the coefficients of graph polynomials such as the independence polynomial, the matching polynomial and the clique polynomial. The independence polynomial of a graph is defined as a polynomial in which its coefficients are the number of independent sets in the graph. The indep...

Let G be a finite group. The probability that any two elements, chosen randomly from a group G, commute is called the commutativity degree of G. The concept of commutativity degree of G plays a major role in determining how much a group is close or far from being abelian. This concept was then extended to the relative commutativity degree of G and...

In DNA splicing system, the potential effects of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and reassociated to produce further molecules are studied. A splicing language depicts the molecules resulting from a splicing system. In this research, a C++ programming code for DNA splicing system with one palindromic...

An independent set of a graph is a set of pairwise non-adjacent vertices. The independence polynomial of a graph is defined as a polynomial in which the coefficient is the number of the independent set in the graph. Meanwhile, a graph of a group G is called conjugate graph if the vertices are non-central elements of G and two distinct vertices are...

The energy of a graph which is denoted by is defined to be the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper we present the concepts of conjugacy class graph of dihedral groups and introduce the general formula for the energy of the conjugacy class graph of dihedral groups. The energy of any dihedral group of...

Exploration of a group's properties is vital for better understanding about the group. Amongst other properties, the homological invariants including the nonabelian tensor square of a group can be explicated by showing that the group is polycyclic. In this paper, the polycyclic presentations of certain crystallographic groups with quaternion point...

A place-labelled Petri net controlled grammar is, in general, a context-free grammar equipped with a Petri net and a function which maps places of the net to productions of the grammar. The languages of place-labelled Petri net controlled grammar consist of all terminal strings that can be obtained by parallel application of the rules of multisets...