It is known that the expansion property of a graph influences the performance of the corresponding code when decoded using iterative algorithms. Certain graph products may be used to obtain larger expander graphs from smaller ones. In particular, the zig-zag product and replacement product may be used to construct infinite families of constant degree expander graphs. This paper investigates the...

Let G(V;E) be a graph. The common neighborhood graph (congraph) of G is a graph with vertex set V , in which two vertices are adjacent if and only if they have a common neighbor in G. In this paper, we obtain characteristics of congraphs under graph operations; Graph :::::union:::::, Graph cartesian product, Graph tensor product, and Graph join, and relations between Cayley graphs and its c...

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...

I.Cahit introduced cordial graphs as a weaker version of graceful and harmonious graphs. The total product cordial labeling is a variant of cordial labeling. In this paper we introduce a vertex analogue product cordial labeling as a variant of total product cordial labeling and name it as total vertex product cordial labeling. Finally, we investigate total vertex product cordial labeling for ma...

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

Many large graphs can be constructed from existing smaller graphs by using graph operations, for example, the Cartesian product and the lexicographic product. Many properties of such large graphs are closely related to those of the corresponding smaller ones. In this short note, we give some properties of the lexicographic products of vertextransitive and of edge-transitive graphs. In particula...

From a set of d-dimensional vectors for some integer d ≥ 1, we obtain a d-dot product graph by letting each vector au correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product au · av ≥ t, for some fixed, positive threshold t. Dot product graphs can be used to model social networks. To understand the position of d-dot product graphs in the land...