6 papers
Combinatorial explanation of the weighted Kirchhoff index of graphs
Wensheng Sun, Yujun Yang, Shou-Jun Xu
Let be a connected graph with vertex set , and let be a positive vertex-weight function satisfying for each $v…
Resistance Curvature: Recognition, Polyhedral Structure, and Graph Products
Meng Guo, Wensheng Sun, Yujun Yang
Resistance curvature, introduced by Devriendt and Lambiotte, is a novel discrete curvature notion defined through effective resistance. A graph is called resistance nonnegative if…
On two conjectures concerning Kemeny's constant of graphs
Wei Li, Wensheng Sun, Yujun Yang
Kemeny's constant for a connected graph , denoted by , is the expected time for a random walk to reach a randomly chosen vertex , regardless of the choice of…
On the Lei--Bai conjecture on -regular Lin--Lu--Yau Ricci-flat graphs
Guangfu Wang, Wensheng Sun, Yujun Yang
We study the Ricci curvature introduced by Lin, Lu, and Yau. A graph is called Ricci-flat if every edge has curvature zero. Lei and Bai classified -regular symmetric Ricci-flat…
A solution to Godsil's conjecture on the edge-connectivity of graphs in association schemes
Wensheng Sun, Yujun Yang, Shou-Jun Xu
A graph is called equiarboreal if the number of spanning trees containing a given edge in is independent of the choice of edge. In [Combinatorica 1(2) (1981) 163--167], God…
On the minimum constant resistance curvature conjecture of graphs
Wensheng Sun, Yujun Yang, Shou-Jun Xu
Let be a connected graph with vertices. The resistance distance between any two vertices and of is defined as the effective resistance between them…