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- W3202904101 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: $mSO_alpha(G) = sum_{uv in E(G)} left[left( d_u^alpha+d_v^alpha right) /2 right]^{1/alpha}$. Here, $uv$ denotes the edge of the graph $G$ connecting the vertices $u$ and $v$, $d_u$ is the degree of the vertex $u$, and $alpha in mathbb{R} backslash {0}$. We also consider the limit cases $mSO_{alphato 0}(G)$ and $mSO_{alphatopminfty}(G)$. Indeed, for given values of $alpha$, 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 $mSO_alpha(G)$ correlates well with several physicochemical properties of octane isomers. Some mathematical properties of mean Sombor indices as well as bounds and new relationships with known topological indices are also discussed." @default.
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- W3202904101 date "2021-10-06" @default.
- W3202904101 modified "2023-09-23" @default.
- W3202904101 title "Mean Sombor index." @default.
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