On the Randić Index of Corona Product Graphs. (3rd November 2011) - Yero Yero, Ismael G. Ismael G.; Rodríguez-Velázquez Rodríguez-Velázquez, Juan A. Juan A.
Abstract : Let G be a graph with vertex set V = ( v 1, v 2, …, v n ) . Let δ ( v i ) be the degree of the vertex v i ∈ V . If the vertices v i 1, v i 2, …, v i h + 1 form a path of length h ≥ 1 in the graph G, then the h th order Randić index R h of G is defined as the sum of the terms 1 / δ ( v i 1 ) δ ( v i 2 ) ⋯ δ ( v i h + 1 ) over all paths of length h contained (as subgraphs) in G . Lower and upper bounds for R h, in terms of the vertex degree sequence of its factors, are obtained for corona product graphs. Moreover, closed formulas are obtained when the factors are regular graphs.