let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-zirodivisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

A divisor graph G is an ordered pair (V, E) where V ⊂ and for all u = v ∈ V , uv ∈ E if and only if u | v or v | u. A graph which is isomorphic to a divisor graph is also called a divisor graph. In this note, we will prove that for any n 1 and 0 m n 2 then there exists a divisor graph of order n and size m. We also present a simple proof of the characterization of divisor graphs which is due to...

In previous literature Coykendall & Maney, as well as Axtell & Stickles, have discussed the concept of irreducible divisor graphs of elements in domains and ring with zero-divisors respectively, with two different definitions. In this paper we seek to look at the irreducible divisor graphs of ring elements under a hybrid definition of the two previous ones—in hopes that this graph will reveal s...

This paper provides further results on the perfect state transfer in integral circulant graphs (ICG graphs). The non-existence of PST is proved for several classes of ICG graphs containing an isolated divisor d0, i.e. the divisor which is relatively prime to all other divisors from d ∈ D \ {d0}. The same result is obtained for classes of integral circulant graphs having the NSF property (i.e. e...

The concept of split domination number was introduced by Kulli and Janakiram. Fink Jacobson the notion k-domination in graphs. In this paper, we acquaint with k-split k-non for some zero-divisor graphs ϑ-Obrazom

In 1988, Beck [10] introduced the notion of coloring of a commutative ring R. Let G be a simple graph whose vertices are the elements of R and two vertices x and y are adjacent if xy = 0. The graph G is known as the zero divisor graph of R. He conjectured that, the chromatic number χ(G) of G is same as the clique number ω(G) of G. In 1993, Anderson and Naseer [1] gave an example of a commutativ...