The spectrum of a Johnson graph is known to be given by the Eberlein polynomial. In this paper, we present a straightforward representation-theoretic derivation of this fact. We also discuss some consequences of this formula, such as the fact that infinitely many of them are Ramanujan. subject classification: spherical functions: 43A90, subgroups of symmetric groups: 20B35, graph theory: 05C99,...

Let G be a nite group. Choose a set S of size k uniformly from G and consider a lazy random walk on the corresponding Cayley graph. We show that for almost all choices of S given k = 2 a log 2 jGj, a > 1, this walk mixes in under m = 2a log a a?1 log jGj steps. A similar result was obtained earlier by Alon and Roichman (see AR]), Dou and Hildebrand (see DH]) using a diierent techniques. We also...

A graph is called cubic and tetravalent if all of its vertices have valency 3 and 4, respectively. It is called vertex-transitive and arc-transitive if its automorphism group acts transitively on its vertex-set and on its arcset, respectively. In this paper, we combine some new theoretical results with computer calculations to construct all cubic vertex-transitive graphs of order at most 1280. ...