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arXiv · 1611.08270

Status connectivity indices and co-indices of graphs and its computation to intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus

Harishchandra S. Ramane·Ashwini S. Yalnaik·Reza Sharafdini
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Abstract

The status of a vertex $u$ in a connected graph $G$, denoted by $σ_G(u)$, is defined as the sum of the distances between $u$ and all other vertices of a graph $G$. The first and second status connectivity indices of a graph $G$ are defined as $S_{1}(G) = \sum_{uv \in E(G)}[σ_G(u)+ σ_G(v)]$ and $S_{2}(G) = \sum_{uv \in E(G)}σ_G(u)σ_G(v)$ respectively, where $E(G)$ denotes the edge set of $G$. In this paper we have defined the first and second status co-indices of a graph $G$ as $\overline{S_{1}}(G) = \sum_{uv \notin E(G)}[σ_G(u)+ σ_G(v)]$ and $\overline{S_{2}}(G) = \sum_{uv \notin E(G)}σ_G(u)σ_G(v)$ respectively. Relations between status connectivity indices and status coindices are established. Also these indices are computed for intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus.

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Harishchandra S. Ramane, Ashwini S. Yalnaik, Reza Sharafdini. 2016-11-24. Status connectivity indices and co-indices of graphs and its computation to intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus. https://arxiv.org/abs/1611.08270

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