Let R be a commutative ring and Z(R) the set of all zero divisors R. Γ(R) is said to divisor graph if x,y ∈ V (Γ(R)) = (x,y) E(Γ(R)) only x.y 0. In this paper, we determine total vertex irregularity strength graphs associated with rings ℤp2 × Zq for p,q prime numbers.

Abstract Let R be a commutative ring with identity. Let G be a graph with vertices as elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper we show that a ring R is finite if and only if clique number of the graph G (associated with R as above) is finite. We also have shown that for a semilocal ring R, the chr...

In a manner analogous to a commutative ring, the L-ideal-based L-zero-divisor graph of a commutative ring R can be defined as the undirected graph Γ(μ) for some L-ideal μ of R. The basic properties and possible structures of the graph Γ(μ) are studied.

Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

Abstract We determine the metric dimension of annihilating-ideal graph a local finite commutative principal ring and with two maximal ideals. also find bounds for an arbitrary ring.