for an arbitrary ring $r$, the zero-divisor graph of $r$, denoted by $gamma (r)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $r$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. it is well-known that for any commutative ring $r$, $gamma (r) cong gamma (t(r))$ where $t(r)$ is the (total) quotient ring of $r$. in this...

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

Crossing number bounds for the mesh of trees graph are derived.

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$.  Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...

Abstract—The solution of non linear problems are based on very well grounded mathematical theories. This document proposes a Newton step graph-based model for convex non linear separable problems (NLP) with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLSP model will grow in a non linear manner. Furthermore, the constraints ha...

In this note we prove lower bounds on the components of the eigenvector associated with the dominant eigenvalue of a graph. These bounds depend only on the eccentricity of the corresponding node and on the eigenvalue As corrollary lower bounds on the dominant eigenvalue are derived, which depend on the diameter of the graph. These bounds were motivated by a heuristic algorithm for finding perip...

We define a construction operation on hypergraphs using a colimit and show that its expressiveness concerning graph rewriting is equal to the graph expressions of Courcelle and the double-pushout approach of Ehrig. With an inductive way of representing graphs, graph rewriting arises naturally as a derived concept. The usefulness of our approach for the compositional modelling of concurrent syst...

A number of mathematical relations for the sextet polynomial are derived. A graph has been introduced (the so called C-graph), representing those properties of a benzenoid system which are essential in the sextet theory of Clar. The main structural properties of the C-graph are determined. The obtained results contribute towards a better understanding of the algebraic and combinatorial backgrou...

We consider the problem of fault tolerance in the graph-state model of quantum computation. Using the notion of composable simulations, we provide a simple proof for the existence of an accuracy threshold for graph-state computation by invoking the threshold theorem derived for quantum circuit computation. Lower bounds for the threshold in the graph-state model are then obtained from known boun...

A new method to clustering analysis, which is based on integration of graph theoretical method and fuzzy objective fimction algorithm, is developed. The connectivity mritriv derived from fuzzy limited neighborhood graph and the measurement for similarity and dissimilarity a re utilized to build a new fuzzy objective function that iinifles global data distribution and local spatial information. ...