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ISRN Discrete MathematicsVolume 2011 2011, Article ID 262183, 7 pages

Research ArticleDepartamento 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 𝛿𝑣𝑖 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-𝛿𝑣𝑖1𝛿𝑣𝑖2⋯𝛿𝑣𝑖ℎ+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.





Autor: Ismael G. Yero and Juan A. Rodríguez-Velázquez

Fuente: https://www.hindawi.com/



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