Table of Contents
ISRN Discrete Mathematics
Volume 2011, Article ID 262183, 7 pages
http://dx.doi.org/10.5402/2011/262183
Research Article

On the Randić Index of Corona Product Graphs

Departamento d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans 26, 43007 Tarragona, Spain

Received 24 July 2011; Accepted 20 September 2011

Academic Editor: X. Yong

Copyright © 2011 Ismael G. Yero and Juan A. Rodríguez-Velázquez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let 𝐺 be a graph with vertex set 𝑉=(𝑣1,𝑣2,…,𝑣𝑛). Let 𝛿(𝑣𝑖) be the degree of the vertex π‘£π‘–βˆˆπ‘‰. If the vertices 𝑣𝑖1,𝑣𝑖2,…,π‘£π‘–β„Ž+1 form a path of length β„Žβ‰₯1 in the graph 𝐺, then the β„Žth order RandiΔ‡ index π‘…β„Ž of 𝐺 is defined as the sum of the terms 1/𝛿(𝑣𝑖1)𝛿(𝑣𝑖2)⋯𝛿(π‘£π‘–β„Ž+1) over all paths of length β„Ž contained (as subgraphs) in 𝐺. Lower and upper bounds for π‘…β„Ž, 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.