English

Cacti with maximum Kirchhoff index

Combinatorics 2015-11-11 v1

Abstract

The concept of resistance distance was first proposed by Klein and Randi\'c. The Kirchhoff index Kf(G)Kf(G) of a graph GG is the sum of resistance distance between all pairs of vertices in GG. A connected graph GG is called a cactus if each block of GG is either an edge or a cycle. Let Cat(n;t)Cat(n;t) be the set of connected cacti possessing nn vertices and tt cycles, where 0tn120\leq t \leq \lfloor\frac{n-1}{2}\rfloor. In this paper, the maximum kirchhoff index of cacti are characterized, as well as the corresponding extremal graph.

Cite

@article{arxiv.1511.03080,
  title  = {Cacti with maximum Kirchhoff index},
  author = {Wen-Rui Wang and Xiang-Feng Pan},
  journal= {arXiv preprint arXiv:1511.03080},
  year   = {2015}
}
R2 v1 2026-06-22T11:41:28.206Z