Revan and hyper-Revan indices of Octahedral and icosahedral networks

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 R₁(G) = ∑<!-- ? -->uv∈<!-- ? -->E$\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[r_G(u) + r_G(v)] and R₂(G) = ∑<!-- ? -->uv∈<!-- ? -->E$\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[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 HR₁(G) = ∑<!-- ? -->uv∈<!-- ? -->E$\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[r_G(u) + r_G(v)]² and HR₂(G) = ∑<!-- ? -->uv∈<!-- ? -->E$\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[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.