1. The Kirchhoff Index of Quasi-Tree Graphs.
- Author
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Xu, Kexiang, Liu, Hongshuang, and Das, Kinkar Ch.
- Subjects
GRAPH connectivity ,TREE graphs ,GEOMETRIC vertices ,LAPLACIAN matrices ,GRAPH theory ,DECISION trees - Abstract
Resistance distance was introduced by Klein and Randić as a generalisation of the classical distance. The Kirchhoff index Kf(G) of a graph G is the sum of resistance distances between all unordered pairs of vertices. In this article we characterise the extremal graphs with the maximal Kirchhoff index among all non-trivial quasi-tree graphs of order n. Moreover, we obtain a lower bound on the Kirchhoff index for all non-trivial quasi-tree graphs of order n. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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