On Half-Transitive Metacirculant Graphs of Prime-Power Order

In this paper, infinitely many graphs of large valency which are half-transitive (that is vertex- and edge-transitive but not arc-transitive) are constructed, and a complete classification is given of half-transitive metacirculant graphs of order a p-power and valency less than 2p, where p is a prime. In particular, it is shown that, for any odd prime p, integers n greater than or equal to 3 and k greater than or equal to 2 such that k divides p-1, are exactly (p(n-2)-1) 2 + p(n-3)-1 nonisomorphic connected half-transitive metacirculants of order p(n) and valency 2k. (C) 2001 Academic Press.