The General Connectivity and General Sum-Connectivity Indices of Nanostructures

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G), di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)= The sum-connectivity index is defined as X(G)= The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies.The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)= andmX(G)= where runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).