On the Randić Index of Corona Product Graphs

Abstract EN

Let G be a graph with vertex set V=(v1,v2,…,vn).

Let δ(vi) be the degree of the vertex vi∈V.

If the vertices vi1,vi2,…,vih+1 form a path of length h≥1 in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1/δ(vi1)δ(vi2)⋯δ(vih+1) over all paths of length h contained (as subgraphs) in G.

Lower and upper bounds for Rh, 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.