On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth

B. Senthilkumar, Y. B. Venkatakrishnan, S. Balachandran, Akbar Ali, Tariq A. Alraqad, Amjad E. Hamza and Elena Guardo

Journal of Mathematics, 2022, vol. 2022, 1-8

Abstract: Let G be a graph having the set of edges EG. Represent by dGu the degree of a vertex u of G. The Sombor (SO) index of G is defined as SOG=∑uv∈EGdGu2+dGv2. The length of a shortest cycle in a graph G is known as the girth of G. A connected graph with the same order and size is usually referred to as a (connected) unicyclic graph. This paper reports the characterization of the graphs possessing the first-two maximum values of the SO index in the class of all (connected) unicyclic graphs with a fixed girth and order.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8202681

DOI: 10.1155/2022/8202681

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