Let R be a fnite commutative ring and N(R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma(R), is the graph obtained by setting all the elements of N(R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x - yin N(R). In this paper, the basic properties of Gamma(R) are investigated and some characterization results regarding co...

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 $I$ be a proper ideal of a commutative semiring $R$ and let $P(I)$ be the set of all elements of $R$ that are not prime to $I$. In this paper, we investigate the total graph of $R$ with respect to $I$, denoted by $T(Gamma_{I} (R))$. It is the (undirected) graph with elements of $R$ as vertices, and for distinct $x, y in R$, the vertices $x$ and $y$ are adjacent if and only if $x + y in P(I)...

In this article, we give several generalizations of the concept of annihilating ideal graph over a commutative ring with identity to modules. Weobserve that over a commutative ring $R$, $Bbb{AG}_*(_RM)$ isconnected and diam$Bbb{AG}_*(_RM)leq 3$. Moreover, if $Bbb{AG}_*(_RM)$ contains a cycle, then $mbox{gr}Bbb{AG}_*(_RM)leq 4$. Also for an $R$-module $M$ with$Bbb{A}_*(M)neq S(M)setminus {0}$, $...

A simple graphoidal cover of a semigraph is such that any two paths in have atmost one end vertex common. The minimum cardinality called the covering number and denoted by . acyclic an In this paper we find for wheel semigraph, unicycle zero-divisor graph.

In this paper, we show that Q n is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Q n is a divisor graph iff k ≥ n− 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn) k is not a divisor graph, where 2 ≤ k ≤ ⌈ 2 ⌉ − 1.