Paper
Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs
Authors
Shaohan Xu, Kexiang Xu, Ivan Damnjanović
Abstract
The number of spanning trees in a graph is the total number of distinct spanning subgraphs of that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and order that attains the maximum number of spanning trees. Moreover, all the bipartite graphs are determined with a given vertex (resp. edge) connectivity and order maximizing the number of spanning trees.