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Extremal values of the Sombor index in unicyclic and bicyclic graphs

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Abstract

Let G be a graph with set of vertices \(V\left( G\right)\) and set of edges  \(E\left( G\right)\). The Sombor index is a recently introduced vertex-degree-based-topological index, defined as

$$SO(G) = \sum\limits_{uv \in E(G)} {\sqrt {{{({d_u})}^2} + {{({d_v})}^2}} } ,$$

where \(d_{u}\) denotes the degree of the vertex u. In this paper we study the extremal values of SO over the set of unicyclic graphs and over the set of bicyclic graphs.

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  1. Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

    Roberto Cruz & Juan Rada

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  1. Roberto Cruz
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  2. Juan Rada
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Correspondence to Roberto Cruz.

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Cruz, R., Rada, J. Extremal values of the Sombor index in unicyclic and bicyclic graphs. J Math Chem 59, 1098–1116 (2021). https://doi.org/10.1007/s10910-021-01232-8

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