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arXiv · 2512.12308

Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs

Shaohan Xu·Kexiang Xu·Ivan Damnjanović
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Abstract

The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ 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.

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Shaohan Xu, Kexiang Xu, Ivan Damnjanović. 2025-12-13. Maximum number of spanning trees and connectivity: Graphs with a fixed minimum degree and bipartite graphs. https://arxiv.org/abs/2512.12308

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