Abstract

Let T(G) be the number of spanning trees in graph G. In this note we explore the asymptotics of T(G) for circulant graphs. The circulant graph Cs1,s2,···,sk n is the 2k regular graph with n vertices labelled 0,1,2, · · ·,n− 1, where node i has the 2k neighbors, (0 ≤ i ≤ n − 1) adjacent to vertices i + s1,i + s2, · · ·,i + sk mod n. In this note we give a closed formula for the asymptotic limit limn→ ∞ T(C s1,s2,···,sk n as a function of s1,s2,...,sn. We then extend this by permitting the si to be linear functions of n, i.e., we give a closed formula for lim n→ ∞ T C

Citations