Characterization of graphs having extremal Randić indices

Abstract: The higher Randić index R t (G) of a simple graph G is defined aswhere δ i denotes the degree of the vertex i and i 1 i 2⋯i t+1 runs over all paths of length t in G. In [J.A. Rodríguez, A spectral approach to the Randić index, Linear Algebra Appl. 400 (2005) 339–344], the lower and upper bound on R 1(G) was determined in terms of a kind of Laplacian spectra, and the lower and upper bound on R 2(G) were done in terms of kinds of adjacency and Laplacian spectra. In this paper we characterize the graphs which achieve the upper or lower bounds of R 1(G) and R 2(G), respectively. [Copyright &y& Elsevier]