Recently, Katre et al. introduced the concept of coprime index a graph. They asked to characterize graphs for which is same as clique number. In this paper, we partially solve problem. fact, prove that number and zero-divisor graph an ordered set ring Zpn coincide. Also, it proved annihilating ideal graphs, co-annihilating comaximal commutative rings can be realized specially constructed posets...

Many authors studied the graph theory in connection with commutative semigroups and commutative and noncommutative rings as we can refer to references. For example, Beck 1 associated to any commutative ring R its zero-divisor graph G R whose vertices are the zero-divisors of R including 0 , with two vertices a, b joined by an edge in case ab 0. Also, DeMeyer et al. 2 defined the zero-divisor gr...

Number theoretic graphs are one of the emerging fields in Graph theory. This article is a study on existing research results graphs, especially Divisor Graphs (DG)s, Function (DFGs) and Cayley (DCGs). We have provided brief survey benchmark findings regarding above-mentioned graphs.

A Sum divisor cordial labeling of a graph G with vertex set V is bijection r from to {1,2,3,...,|V (G )|} such that an edge uv assigned the label 1 if 2 divides r(u)+ (v ) and 0 otherwise; number edges labeled 1differ by at most . sum called graph. In this research paper, we investigate bahevior for Grötzsch graph, fusion any two vertices in duplication arbitrary switching degree four three pat...

In this article we introduce the zero-divisor graphs ?P(X) and ?P? (X) of two rings CP(X) CP? (X); here P is an ideal closed sets in X aggregate those functions C(X), whose support lie on P. analogue ring C?(X). We determine when weakly graph W?P(X) coincides with ?P(X). find out conditions topology X, under-which (respectively, (X)) becomes triangulated/ hypertriangulated. realize that a compl...

Let S be a finite, nonempty set of positive integers. Then, the divisor graph ) (S D of S has S as its vertex set, and vertices i and j are adjacent if and only if either j i or i j . This paper investigates the vertex-chromatic number, the clique number, the clique cover number, and the independence number of ]) ([n D and its complement, where } , 1 : { ] [ Ν ∈ ≤ ≤ = n n i i n . Besides, we di...