From the 1 of 4 linked papers with an AI index.
4 papers
Counting oriented spanning trees in generalized join digraphs
Shaohan Xu, Kexiang Xu
The paper derives formulas for counting oriented spanning trees in generalized join digraphs, expressing the counts in terms of Laplacian eigenvalues of the component digraphs and…
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 DamnjanoviÄ
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…