Revan and hyper-Revan indices of Octahedral and icosahedral networks

Abstract

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) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [rG (u) + rG (v)] and R 2(G) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [rG (u)rG (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) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [rG (u) + rG (v)]2 and HR 2(G) = ∑ u v ∈ E $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$ [rG (u)rG (v)]2. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.