Shaohan Xu

collaborators

3 papers

math.CO2026

Counting oriented spanning trees in generalized join digraphs

Shaohan Xu, Kexiang Xu

Let $G$ be a digraph with vertex set ${1, 2, ..., n}$ and $H_{1}, H_{2}, ..., H_{n}$ be $n$ digraphs. The generalized join digraph $G = G [H_{1}, H_{2}, ..., H_{n}]$ is a di…

math.CO2026

The enumeration of odd spanning trees in graphs

Shaohan Xu, Kexiang Xu

A graph is odd if all of its vertices have odd degrees. In particular, an odd spanning tree in a connected graph is a spanning tree in which all vertices have odd degrees. In this…

math.CO2025

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

Shaohan Xu, Kexiang Xu, Ivan Damnjanović

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 prescrib…