Publication:
Mean Sombor index

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2022
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Shahin Digital Publisher
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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: SOα(G) = P uv∈E(G) [(d α u + d α v ) /2]1/α. Here, uv denotes the edge of the graph G connecting the vertices u and v, du is the degree of the vertex u, and α ∈ R\{0}. We also consider the limit cases mSOα→0(G) and SOα→±∞(G). Indeed, for given values of α, the mean Sombor index is related to well-known opological 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 mSOα(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.
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A Special Volume on Chemical Graph Theory in Memory of Nenad Trinajstic
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Degree-based topological index, Power mean, Sombor indices, QSPR analysis
Bibliographic citation
Mendez-Bermudez, J. A., Aguilar-Sanchez, R., Molina, E. D., & Rodriguez, J. M. (2021). Mean Sombor Index. Discrete mathematics letters, 9, 18-25.