On molecular topological properties of diamond-like networks

The Randic (product) connectivity index and its derivative called the sum-connectivity index are well-known topological indices and both of these descriptors correlate well among themselves and with the π-electronic energies of benzenoid hydrocarbons. The general n connectivity of a molecular graph G is defined as n χ(G)=∑ v i 1 v i 2 v i 3 ... v i n+1 (1/d i 1 d i 2 ... d i n+1 ) and the n sum connectivity of a molecular graph G is defined as n X(G)=∑ v i 1 v i 2 v i 3 ...v i n+1 (1/d i 1 +d i 2 +...+d i n+1 ) , where the paths of length n in G are denoted by v i 1 , v i 2 , ... ,v i n+1 and the degree of each vertex vi is denoted by di. In this paper, we discuss third connectivity and third sum-connectivity indices of diamond-like networks and compute analytical closed results of these indices for diamond-like networks.