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Keywords

Laplacian spectrum, Laplacian-energy-like invariant, Kirchhoff index

Abstract

For a simple connected graph G of order n, having Laplacian eigenvalues μ_1, μ_2, . . . ,μ_{n−1}, μ_n = 0, the Laplacian–energy–like invariant (LEL) and the Kirchhoff index (Kf) are defined as LEL(G) = \sum_{i=1}^{n-1} \sqrt{μ_i} Kf(G) = \sum_{i=1}^{n-1} 1/μ_i, respectively. In this paper, LEL and Kf arecompared, and sufficient conditions for the inequality Kf(G) < LEL(G) are established.

abs_vol31_pp27-41.pdf (32 kB)
Abstract

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