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- W4200320807 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." @default.
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- W4200320807 date "2022-03-01" @default.
- W4200320807 modified "2023-10-18" @default.
- W4200320807 title "A relation between a vertex-degree-based topological index and its energy" @default.
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- W4200320807 doi "https://doi.org/10.1016/j.laa.2021.11.021" @default.
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