On the number of spanning trees in directed circulant graphs

Let gk(n) [respectively, fk(n)] be the maximum number of spanning trees in directed circulant graphs (respectively, regular directed graphs) with n vertices and out-degrees equal to k > 1. We show that gk(n) = kn(1+o(1)) and fk(n) = kn(1+o(1)). Moreover, we prove that g2(n) = ⌊(2n + 1)/3⌋. © 2001 John Wiley & Sons, Inc.