# Sanhan KhasrawSalahaddin University - Erbil | SUH · Department of Mathematics

Sanhan Khasraw

PhD

## About

20

Publications

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32

Citations

Citations since 2016

## Publications

Publications (20)

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...

For a finite group G, the intersection graph of G is the graph whose vertex set is the set of all proper non-trivial subgroups of G, where two distinct vertices are adjacent if their intersection is a non-trivial subgroup of G. In this article, we investigate the detour index, eccentric connectivity, and total eccentricity polynomials of the inters...

For a finite group G, the co-prime order graph Θ(G) of G is defined as the graph with vertex set G, the group itself, and two distinct vertices u, v in Θ(G) are adjacent if and only if gcd(o(u), o(v)) = 1 or a prime number. In this paper, some properties and some topological indices such as Wiener, Hyper-Wiener, first and second Zagreb, Schultz, Gu...

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...

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...

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...

Let $G$ be a finite group. The intersection graph of $G$ is a graph whose vertex set is the set of all proper non-trivial subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $H\cap K \neq \{e\}$, where $e$ is the identity of the group $G$. In this paper, we investigate some properties and exploring some topological in...

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...

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...

For a nonabelian group G, the non-commuting graph $\Gamma_G$ of $G$ is defined as the graph with vertex set $G-Z(G)$, where $Z(G)$ is the center of $G$, and two distinct vertices of $\Gamma_G$ are adjacent if they do not commute in $G$. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of non-...

In this paper, the probability that two elements of a finite ring have product zero is considered. The bounds of this probability are found for an arbitrary finite commutative ring with identity 1. An explicit formula for this probability in the case of n Z , the ring of integers modulo n , is obtained.

Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and simplicity; and (2) sum decompositions.

An axial algebra is a commutative non-associative algebra generated by axes, that is, primitive, semisimple idempotents whose eigenvectors multiply according to a certain fusion law. The Griess algebra, whose automorphism group is the Monster, is an example of an axial algebra. We say an axial algebra is of Monster type if it has the same fusion la...

Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and simplicity; and (2) sum decompositions.

An extension of the concept of commutativity degree named the probability that an element of a group fixes a set was introduced in 2013. Suppose is a metacyclic 5-group and is the set of all ordered pairs (x,y) in G*G such that lcm(|x|,|y|)=5, xy=yx and x is not equal to y. In this paper, the probability that an element of a metacyclic 5-group fixe...

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.

The main result of this thesis concerns the classification of 3-generated M-axial algebras A such that every 2-generated subalgebra of A is a Sakuma algebra of type N X, where N ∈ {2, 3, 4} and X ∈ {A, B, C}. This goal requires the classification of all groups G which are quotients of the groups T (s 1 ,s 2 ,s 3) = x, y, z | x 2 , y 2 , z 2 , (xy)...

This thesis is the classification of the Majorana algebras of the symmetric group S 4 of degree 4. There are twelve shapes in total for this group. Four of them are considered in [9]. We deal with six shapes not covered in [9], describe the resulting algebras and support our claims with hand and computer calculations. The two shapes not covered her...

## Projects

Project (1)