From the 1 of 6 linked papers with an AI index.
6 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…
Edge transmission irregular graphs
Kexiang Xu, Ivan DamnjanoviÄ, UroÅ¡ MilivojeviÄ +1
The transmission of a vertex in a connected graph is the sum of distances from to all vertices in . A transmission irregular (TI) graph is a connected graph in which…
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…
On the transmission irregular trees with the maximum Wiener index
Ivan DamnjanoviÄ, Anran Xu, Kexiang Xu
The transmission of a vertex in a (chemical) graph is the sum of distances from to other vertices in . If any two vertices of have different transmissions, then…
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…