Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stolarsky-Puebla index   We introduce a degree-based variable topological index inspired on the
Stolarsky mean (known as the generalization of the logarithmic mean). We name
this new index as the Stolarsky-Puebla index: $SP_\alpha(G) = \sum_{uv \in
E(G)} d_u$, if $d_u=d_v$, and $SP_\alpha(G) = \sum_{uv \in E(G)} \left[\left(
d_u^\alpha-d_v^\alpha\right)/\left(
\alpha(d_u-d_v\right)\right]^{1/(\alpha-1)}$, otherwise. Here, $uv$ denotes the
edge of the network $G$ connecting the vertices $u$ and $v$, $d_u$ is the
degree of the vertex $u$, and $\alpha \in \mathbb{R} \backslash \{0,1\}$.
Indeed, for given values of $\alpha$, the Stolarsky-Puebla index reproduces
well-known topological indices such as the reciprocal Randic index, the first
Zagreb index, and several mean Sombor indices. Moreover, we apply these indices
to random networks and demonstrate that $\left< SP_\alpha(G) \right>$,
normalized to the order of the network, scale with the corresponding average
degree $\left< d \right>$.

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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas