Mean Sombor index

J. A. Me´ndez-Bermu´ dez; R. Aguilar-Sa´ nchez; Edil D. Molina; Jose´ M. Rodr´ıguez

doi:10.47443/dml.2021.s204

Author(s)

J. A. Me´ndez-Bermu´ dez Instituto de F ́ısica, Beneme ́rita Universidad Auto ́noma de Puebla,Apartado Postal J-48, Puebla 72570,Mexico

R. Aguilar-Sa´ nchez Facultad de Ciencias Qu ́ımicas, Beneme ́rita Universidad Auto ́noma de Puebla,Puebla 72570,Mexico

Edil D. Molina Facultad de Matem a ́ticas, Universidad Auto ́noma de Guerrero, Carlos E. Adame No.54 Col. Garita,Acapulco Gro. 39650,Mexico

Jose´ M. Rodr´ıguez Departamento de Matem a ́ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30,28911 Legane ́s, Madrid,Spain

Abstract

We introduce a degree-based variable topological index inspired on the power (or generalized) mean. We name this new index as the mean Sombor index: mSO (G) = Puv2E(G) [(du + dv ) =2]1= . Here, uv denotes the edge of the graph G connecting the vertices u and v, du is the degree of the vertex u, and 2 Rnf0g. We also consider the limit cases mSO !0(G) and mSO ! 1(G). Indeed, for given values of , the mean Sombor index is related to well-known topological indices such as the inverse sum indeg index, the reciprocal Randic´ index, the first Zagreb index, the Stolarsky-Puebla index and several Sombor indices. Moreover, through a quantitative structure property relationship (QSPR) analysis we show that mSO (G) correlates well with several physicochemical properties of octane isomers. Some mathematical properties of the mean Sombor index as well as bounds and new relationships with known topological indices are also discussed.

Publication Details

Page(s) 18-25

DOI 10.47443/dml.2021.s204

Published Journal: Discrete Mathematics Letters, Volume: 9, Issue: 0, Year: 2022

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Keywords

Sombor indices, degree-based topological index, power mean, QSPR analysis