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Available online: February 27, 2018

Revan and hyper-Revan indices of Octahedral and icosahedral networks

Abdul Qudair Baig, Muhammad Naeem, Wei Gao
Volume 3 - Issue 1.     Year 2018.     Pages 33–40.

DOI: 10.21042/AMNS.2018.1.00004

Abstract

Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Recently, the Revan vertex degree concept is defined in Chemical Graph Theory. The first and second Revan indices of $G$ are defined as $R_{1}(G)=\sum\limits_{uv\in E}[r_{G}(u)+r_{G}(v)]$ and $R_{2}(G)=\sum\limits_{uv\in E}[r_{G}(u)r_{G}(v)]$, where $uv$ means that the vertex $u$ and edge $v$ are adjacent in $G$. The first and second hyper-Revan indices of $G$ are defined as $HR_{1}(G)=\sum\limits_{uv\in E}[r_{G}(u)+r_{G}(v)]^{2}$ and $HR_{2}(G)=\sum\limits_{uv\in E}[r_{G}(u)r_{G}(v)]^{2}$. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

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ISSN:
2444-8656
Category:
Applied Mathematics, Nonlinear Sciences

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