A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits of equal size. In this paper, we give a characterization of cubic nonCayley vertex-transitive bi-Cayley graphs over a regular p-group, where p > 5 is a prime. As an application, a classification of cubic non-Cayley vertex-transitive graphs of order 2p3 is given for each prime p.

1. Dejter, I., Giudici, R.E.: On Unitary Cayley graphs, JCMCC, 18,121-124. 2. Brrizbitia, P and Giudici, R.E. 1996, Counting pure k-cycles in sequence of Cayley graphs, Discrete math., 149, 11-18. 3. Madhavi, L and Maheswari, B.2009, Enumeration of Triangles and Hamilton Cycles in Quadratic residue Cayley graphas, Chamchuri Journal of Mathematics, 1,95-103. 4. Madhavi, L and Maheswari, B. 2010,...

Let us say that a Cayley graph of a group G of order n is a Černý Cayley graph if every synchronizing automaton containing as a subgraph with the same vertex set admits a synchronizing word of length at most (n− 1)2. In this paper we use the representation theory of groups over the rational numbers to obtain a number of new infinite families of Černý Cayley graphs.

Given an integer n, one defines the unitary Cayley graph, denoted Cay(Zn,Zn), to be the graph whose vertex set is Zn, the integers modulo n, with an edge between two vertices x, y if x− y is a unit in (the ring) Zn. Unitary Cayley graphs have been studied as objects of independent interest (see, for example, [3], [2], [7], [8], [9]) but are of particular relevance in the study of graph represen...

Recently, several works by a number of authors have studied integrality, distance and powers Cayley graphs over some finite groups, such as dicyclic groups (generalized) dihedral groups. Our aim is to generalize and/or give analogues these results for generalized For example, we necessary sufficient condition graph group be integral (i.e., all eigenvalues its adjacency matrix are in Z). We also...

Graph Theory has been realized as one of the most useful branches of Mathematics of recent origin, finding widest applications in all most all branches of sciences, social sciences, and engineering and computer science. Nathanson[8] was the pioneer in introducing the concepts of NumberTheory, particularly, the “Theory of congruences” i n Graph Theory, thus paving way for the emergence of a new ...

The point we try to get across is that the generalization of the counterparts of the matroid theory in Cayley graphs since the matroid theory frequently simplify the graphs and so Cayley graphs. We will show that, for a Cayley graph ΓG, the cutset matroid M ∗(ΓG) is the dual of the circuit matroid M(ΓG). We will also deduce that if Γ ∗ G is an abstract-dual of a Cayley graph Γ, then M(Γ∗ G ) is...

We introduce a new class of fixed-degree interconnection networks, called the Cayley graph connected cycles , which includes the well known cube-connected cycles as a special case. This class of networks is shown to be vertexsymmetric and maximally fault tolerant (if the given Cayley graph is maximally fault tolerant). We propose simple routing and broadcasting algorithms for these networks in ...