On Rehan-Lanel Indices of Graphs

A graph G is made up of vertices $V(G)$ and edges $E(G)$. In this paper, we propose two new indices defined as, RL₃(G)=∑uv∈ E(G)( dG(u)-dG(v)+ dG(u)dG(v) ) and RL₄(G)=∑uv∈ E(G)( | dG(u)-dG(v)| dG(u)dG(v)). We named first index as third Rehan-Lanel index of G (RL₃) and second index as fouth Rehan-Lanel index of G (RL₄). dG(u) and dG(v) denote the degrees of the vertices u, v ∈ V(G). Based on these new indices and the definitions of Revan degree, Domination degree, Banhatti degree, Temperature of a vertex, KV indices. We subsequently introduced an additional 222 indices/exponentials to Chemical Graph Theory and computed results for RL₁, RL₂, the third and fourth E- Banhatti Rehan-Lanel indices, the third and fourth Revan Rehan-Lanel indices, third and fourth Domination Rehan-Lanel indices,third and fourth temperature Rehan-Lanel indices, third and fourth Rehan-Lanel KV indices, and third and fourth neighborhood Rehan-Lanel indices for the standard graphs such as $r-$ regular graph, complete graph, cycle, path and compete bipartite graph. Apart from these indices, here we define the fifth and sixth Rehan-Lanel indices incorporating with first and the second zagreb indices and closeness centrality of a vertex of a graph. Also, we introduce the seventh, eighth, ninth and tenth Rehan-Lanel indices based on forgotten index, Sombor index, Nirmala index and Albertson index of a graph respectively. Furthermore, we conduted calculations for Wheel graph, Sunflower graph and French Windmill graph. These new indices would be helpful in QSPR/QSAR studies.