On q-connected chordal graphs with minimum number of spanning trees

Abstract

Let k be the largest integer such that m ≥for some positive integers n, m, q. Let S(q, n, m) be a set of all q-connected chordal graphs on n vertices and m edges for n−k 2 ≥ q ≥ 2. Let t(G) be the number of spanning trees in graph G. We identify G ∈ S(q, n, m) such that t(G) < t(H) for any H that satisfies H ∈ S(q, n, m) and H ≇ G. In addition, we give a sharp lower bound for the number of spanning trees of graphs in S(q, n, m).