Bipancyclic properties of Cayley graphs generated by transpositions

Connectivity Properties of Oriented Cayley Graphs Generated by Transpositions

On the automorphism group of Cayley graphs generated by transpositions

The modified bubble-sort graph of dimension n is the Cayley graph of Sn generated by n cyclically adjacent transpositions. In the present paper, it is shown that the automorphism group of the modified bubble sort graph of dimension n is Sn × D2n, for all n ≥ 5. Thus, a complete structural description of the automorphism group of the modified bubble-sort graph is obtained. A similar direct produ...

Rotational Cayley Graphs on Transposition Generated Groups

As it is introduced by Bermond, Kodate, and Prennes, some Cayley graphs, including most popular models for interconnection networks, admit a special auto-morphism, called complete rotation. Such an automorphism is often used to derive algorithms or properties of the underlying graph. For example, optimal gossiping algorithms can be easily designed, and the constructions of the best known edge d...

On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

Given a finite simple graph G with n vertices, we can construct the Cayley graph on the symmetric group Sn generated by the edges of G , interpreted as transpositions. We show that, if G is complete multipartite, the eigenvalues of the Laplacian of Cay(G ) have a simple expression in terms of the irreducible characters of transpositions and of the Littlewood–Richardson coefficients. As a conseq...

Cayley graphs and symmetric interconnection networks

These lecture notes are on automorphism groups of Cayley graphs and their applications to optimal fault-tolerance of some interconnection networks. We first give an introduction to automorphisms of graphs and an introduction to Cayley graphs. We then discuss automorphism groups of Cayley graphs. We prove that the vertex-connectivity of edge-transitive graphs is maximum possible. We investigate ...