Improved bounds for Kirchhoff index of graphs

Document Type : Original paper

Authors

1 No

2 Faculty of Electronic Engineering, University of Niš, Niš, Serbia

Abstract

Let $G$ be a simple connected graph with n vertices. The Kirchhoff index of $G$ is defined as $Kf (G) = n\sum_{i=1}^{n-1}1/μ_i$, where $\mu_1\ge \mu_2\ge \dots\ge \mu_{n-1}>\mu_n=0$ are the Laplacian eigenvalues of $G$. Some bounds on $Kf (G)$ in terms of graph parameters such as the number of vertices, the number of edges, first Zagreb index, forgotten topological index, etc., are presented. These bounds improve some previously known bounds in the literature.

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 1
March 2023
Pages 243-251

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