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https://scidar.kg.ac.rs/handle/123456789/13879
Title: | A relation between a vertex-degree-based topological index and its energy |
Authors: | Gutman, Ivan ![]() ![]() Monsalve, Juan ![]() Rada, Juan ![]() |
Issue Date: | 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. |
URI: | https://scidar.kg.ac.rs/handle/123456789/13879 |
Type: | article |
DOI: | 10.1016/j.laa.2021.11.021 |
ISSN: | 0024-3795 |
SCOPUS: | 2-s2.0-85120917868 |
Appears in Collections: | Faculty of Science, Kragujevac |
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