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

Nor Haniza Sarmin

Ph D (Mathematics)

## About

484

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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 (484)

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...

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...

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...

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...

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...

A fuzzy subset A defined on a set X is represented as A = {(x, A (x), where x ∈ X}. It is not always possible for membership functions of type λA : X → [0,1] to associate with each point x in a set X a real number in the closed unit interval [0,1] without the loss of some useful information. The importance of the ideas of “belongs to” (∈) and “quas...

The advancement in the fascinating area of fuzzy set theory has become area of much interest, generalization of the existing fuzzy subsystems of other algebraic structures is very important to tackle more current real life problems. In this paper, we give more generalized form of regular ordered gamma semigroups in terms of (E,EVq_k)-fuzzy gamma id...

Let í µí°º be a metacyclic 2-group and Γ í µí°º is the graph of í µí°º. The adjacency matrix of Γ í µí°º is a matrix í µí°´=µí°´= [í µí± í µí±í µí± ] consisting of 0′í µí± and 1′í µí± in which the entry í µí± í µí±í µí± is 1 if there is an edge between the í µí± í µí±¡ℎ and í µí± í µí±¡ℎ vertices and 0 otherwise. The energy of a graph is th...

The intuitionistic fuzzification of the notion of an interior ideal in ordered semigroups is considered. The purpose of this study is to introduce the notion of (∈, ∈ vq)-intuitionistic fuzzy interior ideals and (∈, ∈)-intuitionistic fuzzy nterior ideals of semigroups. The important milestone of the present paper is to link ordinary intuitionistic...

Bieberbach groups are torsion free crystallographic groups. In this paper, our focus is on the Bieberbach groups with elementary abelian 2-group point group, The central subgroup of the nonabelian tensor square of a group is generated by for all in The purpose of this paper is to compute the central subgroups of the nonabelian tensor squares of two...

A crystallographic group is a discrete subgroup of the set of isometries of Euclidean space where the quotient space is compact. A torsion free crystallographic group, or also known as a Bieberbach group has the symmetry structure that will reveal its algebraic properties. One of the algebraic properties is its nonabelian tensor square. The nonabel...

Let be a metacyclic 3-group and let be a non-empty subset of such that . The generalized commuting and non-commuting graphs of a group is denoted by and respectively. The vertex set of the generalized commuting and non-commuting graphs are the non-central elements in the set such that where Two vertices in are joined by an edge if they commute, mea...

An independent set of a graph is a set of pairwise non-adjacent vertices while the independence number is the maximum cardinality of an independent set in the graph. 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...

Let G be a metacyclic 5-group and Ω is the set of all ordered pairs (x, y) in G × G such that lcm(|x|, |y|) = 5, xy = yx and x ≠ y. In this paper, the probability that an element of G fixes a set Ω is determined by using conjugation action. The results obtained are then applied to graph theory, more precisely to the orbit graph.

Graphs can be related to groups by looking at its vertices and edges. The vertices are comprised of the elements or sets from the groups and the edges are the properties and conditions for the graph. Recently, research on graphs of groups have attracted many authors. A conjugate graph of a group is defined as; its vertex set is the set of non-centr...

Let G be a metacyclic 2-group and gamma(conj,G) is the conjugate graph of G. The vertices of gamma(conj,G) are non-central elements in which two vertices are adjacent if they are conjugate. The adjacency matrix of gamma(conj,G) is a matrix A=[a(i,j)] consisting 0's and 1's in which the entry a(i,j) is 1 if there is an edge between ith and jth verti...

Let G be a dihedral group and Gamma its conjugacy class graph. The Laplacian energy of the graph, LE(Gamma) 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 number of vertices. In this research, the Laplacian matrices of the conjugacy class graph...

A graph is a mathematical structure which consists of vertices and edges that is used to model relations between object. In this research, the generalized conjugacy class graph is constructed for some dihedral groups to show the relation between orbits and their cardinalities. In order to construct the graph, the probability that an element of the...

Let H be a subgroup of a finite group G. The co-prime graph of a group is defined as a graph whose vertices are elements of G and two distinct vertices are adjacent if and only if the greatest common divisor of order of x and y is equal to one. This concept has been extended to the relative co-prime graph of a group with respect to a subgroup H, wh...

Let G be a metacyclic p-group where p is either 3 or 5, and let Ω be the set of all ordered pairs (x, y) in G × G such that lcm(|x|,|y|)=p, xy = yx and x ≠ y. In this paper, the conjugate graphs associated to metacyclic 3-groups and metacyclic 5-groups are found. Besides, the generalized conjugacy class graphs of these groups are also determined. W...

The operation of insertion has been studied extensively throughout the years for its impact in many areas of theoreticalcomputer science such as DNAcomputing. First introduced as a generalization of the concatenation operation, many variants of insertion have been introduced, each with their own computational properties. In this paper, we introduce...

The structure of ordered Γ-semigroup is a generalization of ordered semigroup. The purpose of this paper is to introduce the notion of (∈,∈Vqk) - fuzzy bi Γ-ideals in ordered Γ-semigroup. This new concept is the generalization of fuzzy bi-ideals of ordered semigroup. Further we explore some classifications of different classes such as regular, righ...

In mathematics, the energy of a graph is the sum of the values of the eigenvalues of the adjacency matrix of the graph. This quantity is studied in the context of spectral graph theory. In this paper the concepts of non-commuting graph of dihedral groups are presented and the general formula for the energy of this associated graph is found.