Abstract
The Kirchhoff index of a graph G is the sum of resistance distances between all unordered pairs of vertices, which was introduced by Klein and Randić. In this paper, we characterize all extremal graphs with respect to Kirchhoff index among all graphs obtained by deleting p edges from a complete graph
with
and obtain a sharp upper bound on the Kirchhoff index of these graphs. In addition, all the graphs with the first to ninth maximal Kirchhoff indices are completely determined among all connected graphs of order
.
Acknowledgments
The authors are much grateful to two anonymous referees for their valuable comments on our paper, which have considerably improved the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.