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Mathematical Communications, Vol. 15 No. 2, 2010.

Original scientific paper

Cacti with minimum, second-minimum, and third-minimum Kirchhoff indices

Hongzhuan Wang ; Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, Jiangsu, P. R. China
Hongbo Hua ; Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, Jiangsu, P. R. China
Dongdong Wang ; Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, Jiangsu, P. R. China

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Abstract

Resistance distance was introduced by Klein and
Randić. The Kirchhoff index Kf(G) of a graph G is the
sum of resistance distances between all pairs of vertices. A graph
G is called a cactus if each block of G is either an edge or a
cycle. Denote by Cat(n; t) the set of connected cacti possessing
n vertices and t cycles. In this paper, we give the first three
smallest Kirchhoff indices among graphs in Cat(n; t), and
characterize the corresponding extremal graphs as well.

Keywords

cactus; Kirchhoff index; resistance distance

Hrčak ID:

61811

URI

https://hrcak.srce.hr/61811

Publication date:

8.12.2010.

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