Abstract: | Let GF(q) be a finite field of q elements. Let G denote the group of matrices M(x, y) = (y x0 1) over GF(q) with y ≠ 0. Fix an irreducible polynomial For each a ϵ GF(q), let Xa be the graph whose vertices are the q2 − q elements of G, with two vertices M(x, y), M(v, w) joined by an edge if and only if The graphs Xa with a ϵ/ {0, t2 − 4n} are (q + 1)-regular connected graphs which have received recent attention, as they've been shown to be Ramanujan graphs. We determine the diameter of these graphs Xa. © 1996 John Wiley & Sons, Inc. |