On the spectrum of Wenger graphs.

Abstract: Let , where p is a prime and is an integer. For , let P and L be two copies of the -dimensional vector spaces over the finite field . Consider the bipartite graph with partite sets P and L defined as follows: a point is adjacent to a line if and only if the following m equalities hold: for . We call the graphs Wenger graphs. In this paper, we determine all distinct eigenvalues of the adjacency matrix of and their multiplicities. We also survey results on Wenger graphs. [Copyright &y& Elsevier]