A divisor cordial labeling of a graph G with vertex set V vertex G is a bijection f from V to {1, 2, 3, . . . |V|} such that an edge uv is assigned the label 1 if f(u) divides f(v) or f(v)divides f(u) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a divisor cordial labeling, then it is called divisor cordial gr...

Let G = Γ(S) be a semigroup graph, i.e., zero-divisor graph of S with zero element 0. For any adjacent vertices x, y in G, denote C(x,y) {z∈V(G) | N (z) {x,y}}. Assume that there exist two y, vertex s∈C(x,y) and z such d (s,z) 3. This paper studies algebraic properties graphs Γ(S), giving some sub-semigroups ideals S. It constructs classes classifies all the property cases.

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R) = A(R)r {0} and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal...

The paper studies the characterization of adjacency matrix corresponding to zero-divisor graphs of finite commutative ring of Gaussian integer under modulo „n‟. For each positive integer we calculate number of zerodivisors & examine nature of the matrix, and then we generalized the order of matrix in each case. Firstly, we have started with some example, which motivates the later results. The s...

In this note we prove that in the case of finitely generated amenable groups the classical zero divisor conjecture implies the analytic zero divisor conjecture of Linnell.

The field of mathematics that studies the relationship between algebraic structures and graphs is known as graph theory. It incorporates concepts from theory, which examines characteristics topology graphs, with those abstract algebra, deals such groups, rings, fields. If vertex set a G^ fully made up zero divisors modular ring Zn, said to be zero-divisor graph. products two vertices are equal ...