Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs
Combinatorics
2025-12-16 v1
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.
Cite
@article{arxiv.2512.12308,
title = {Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs},
author = {Shaohan Xu and Kexiang Xu and Ivan Damnjanović},
journal= {arXiv preprint arXiv:2512.12308},
year = {2025}
}