Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the “Theory of Congruences” in Graph Theory. Thus he paved the way for the emergence of a new class of graphs, namely “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes a...

We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for sufficiently large k and infinitely many values of d, Cayley graphs and digraphs of diame...

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,...

We explicitly determine all of the transitive groups of degree p2, p a prime, whose Sylow p-subgroup is not isomorphic to the wreath product Z p Z p . Furthermore, we provide a general description of the transitive groups of degree p2 whose Sylow p-subgroup is isomorphic to Z p Z p , and explicitly determine most of them. As applications, we solve the Cayley Isomorphism problem for Cayley objec...

In this paper, we have obtained the total chromatic number of some classes Cayley graphs, odd graphs and mock threshold graphs.

The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study...

A graph is one-regular if its automorphism group acts regularly on the arc set. In this paper, we construct a new infinite family of one-regular Cayley graphs of any prescribed valency. In fact, for any two positive integers , k 2 except for ( , k) ∈ {(2,3), (2,4)}, the Cayley graph Cay(Dn,S) on dihedral groups Dn = 〈a, b | an = b2 = (ab)2 = 1〉 with S = {a1+ +···+ t b | 0 t k − 1} and n = ∑k−1 ...