On the General Randi\'c index of polymeric networks modelled by generalized Sierpi\'nski graphs

The General Randi'c index $R_{\alpha }$ of a simple graph $G$ is defined as $$R_{\alpha }(G)=\sum _{v_i\sim v_j}({\delta }_i{\delta }_j{)}^{\alpha },$$ where ${\delta }_i$ denotes the degree of the vertex $v_i$. Rodr'iguez-Vel'azquez and Tom'as-Andreu [MATCH Commun. Math. Comput. Chem. 74 (1) (2015) 145–160] obtained closed formulae for the Randi'c index $R_{-1\mathrm{/}2}$ of Sierpi'nski-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 Randi'c index $R_{\alpha }$ of Sierpi'nski-type polymeric networks, where the base graph is arbitrary.