A note on Cayley graphs

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

A note on orbit graphs of finite groups and colour-clique graphs of Cayley graphs

Let G be a (finite) group and let S be a non-empty subset of G. The vertex set of the orbit graph O(G,S) is the union, over all s ∈ S, of orbits of left translations induced by s. If u and v are distinct vertices (each representing an orbit of some s and t from S), then for any g ∈ G appearing in both orbits there is an edge coloured g in O(G,S) joining u and v. Orbit graphs are an important sp...

On the distance eigenvalues of Cayley graphs

In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...

A Note on Strongly Quotient Graphs