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Title: A relation between a vertex-degree-based topological index and its energy
Authors: Gutman I.
Monsalve, Juan
Rada, Juan
Journal: Linear Algebra and Its Applications
Issue Date: 1-Mar-2022
Abstract: Let G be a simple graph with vertex set V and edge set E, and let di be the degree of the vertex vi∈V. If the vertices vi and vj are adjacent, we denote the respective edge by vivj∈E. A vertex-degree-based topological index φ is defined as φ(G)=∑vivj∈Eφdi,dj, where φi,j is a function with the property φi,j=φj,i. The general extended adjacency matrix Aφ is defined as [Aφ]ij=φdi,dj if vivj∈E, and 0 otherwise. The energy associated to φ of G is the sum of the absolute values of the eigenvalues of Aφ. In this paper we show that ρ(G)Eφ(G)≥2φ(G) for all connected graphs G, where ρ(G) is the spectral radius of G and φa,b≠0 for all a,b∈N. We also characterize the graphs where equality holds. As a consequence, for any tree T with n vertices, Eφ(T)≥2n−1φ1,(n−1), with equality holding if and only if T≅Sn.
Type: journal article
DOI: 10.1016/j.laa.2021.11.021
ISSN: 00243795
SCOPUS: 85120917868
Appears in Collections:University Library, Kragujevac

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