Sum of powers of the Laplacian eigenvalues and the kirchhoff index of a graph

Mingying Hu, Haiyan Chen and Wenwen Sun

Applied Mathematics and Computation, 2023, vol. 446, issue C

Abstract: Let G=(V,E) be a simple connected graph with vertex set V={1,2,…,n}. For any real number α, the topological index sα(G) of G is defined assα(G)=∑i=1n−1μiα,where μ1≥μ2≥…μn−1>μn=0 are the Laplacian eigenvalues of G. In this paper, we first express sα(G) explicitly in terms of resistance distances Ωij,i,j∈V. Then we generalize the following well-known equalityns−1(G)=Kf(G)to any integer k≥−1, where Kf(G)=∑iKeywords: Laplacian eigenvalue; Resistance distance; Kirchhoff index; First Zagreb index; Laplacian Estrada index (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000528

DOI: 10.1016/j.amc.2023.127883

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