5 papers
A Turán-type extremal problem for the number of spanning trees in -free graphs
Shaohan Xu, Fengming Dong, Kexiang Xu
For a graph \(F\), the Turán number \(\ex(n,F)\) is the maximum number of edges in an \(F\)-free graph on \(n\) vertices. Let \(q\ge 2\) be an integer and set \(n=q^{2}+q+1\). Brow…
Counting oriented spanning trees in generalized join digraphs
Shaohan Xu, Kexiang Xu
Let be a digraph with vertex set and be digraphs. The generalized join digraph is a di…
On asymptotic values for the minimum number of spanning forests in simple regular graphs
Shaohan Xu, Kexiang Xu
Let be the number of spanning forests in a graph and be the set of all connected -regular simple graphs of order . Define $\widehat{f}_{d}=\limi…
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…
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 is the total number of distinct spanning subgraphs of that are trees. In this paper we characterize the unique graph with a prescrib…