On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs

Abstract

The General Randić index $R_{\alpha }$ of a simple graph $G$ is defined as \[ R_α(G)=\sum_{v_{i}\sim v_{j}} (δ_{i}δ_{j})^α, \] where ${\delta }_i$ denotes the degree of the vertex $v_i$. Rodríguez-Velázquez and Tomás-Andreu [MATCH Commun. Math. Comput. Chem. 74 (1) (2015) 145--160] obtained closed formulae for the Randić index $R_{-1/2}$ of Sierpiński-type polymeric networks, where the base graph is a complete graph, a triangle-free regular graph or a bipartite semiregular graph. In the present article we obtain closed formulae for the general Randić index $R_{\alpha }$ of Sierpiński-type polymeric networks, where the base graph is arbitrary.