In a manner analogous to a commutative ring, the idealbased zero-divisor graph of a commutative semiring R can be defined as the undirected graph ΓI(R) for some ideal I of R. The properties and possible structures of the graph ΓI (R) are studied.

In this article, we obtain an upper bound for the regularity of binomial edge ideal a graph whose every block is either cycle or clique. As consequence, cactus graph. We also identify certain subclass attaining bound.

We determine the arithmetical rank of every edge ideal of a Ferrers graph.

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.

The Graph Minor Theorem of Robertson and Seymour establishes nonconstructively that many natural graph properties are characterized by a nite set of forbidden substructures, the obstructions for the property. We prove several general theorems regarding the computation of obstruction sets from other information about a family of graphs. The methods can be adapted to other partial orders on graph...

Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...

17 graph. The cuts of G are the minimal dependent sets of a matroid T ? (G) on the edge set E. A matroid T is cographic if there exists some graph G such that T is isomorphic to the cut matroid T ? (G). Every cographic matroid is representable over any eld 18]. Therefore if an access structure A has a cographic appropriate matroid, then A is universally ideal. Unlike graphic matroids, we do not...