1 research outputs found
The second eigenvalue of some normal Cayley graphs of high transitive groups
Let be a finite group acting transitively on ,
and let be a Cayley graph of . The graph
is called normal if is closed under conjugation. In this paper, we obtain
an upper bound for the second (largest) eigenvalue of the adjacency matrix of
the graph in terms of the second eigenvalues of certain subgraphs of
(see Theorem 2.6). Using this result, we develop a recursive method to
determine the second eigenvalues of certain Cayley graphs of and we
determine the second eigenvalues of a majority of the connected normal Cayley
graphs (and some of their subgraphs) of with , where is the set of
points in non-fixed by .Comment: 26 page