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On the conjecture of Delorme, Favaron and Rautenbach about the Randic index [An article from: European Journal of Operational Research]
Book Details
Author(s)L. Pavlovic
PublisherElsevier
ISBN / ASINB000PDSPQS
ISBN-13978B000PDSPQ2
AvailabilityAvailable for download now
MarketplaceUnited States 🇺🇸
Description
This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2007. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.
Description:
Let G(k,n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randic index @g=@g(G) of a graph G is defined by: @g=@?"("u"v")(@d"u@d"v)^-^1^/^2, where @d"u is the degree of vertex u and the summation extends over all edges (uv) of G. In this paper we prove the conjecture of Delorme, Favaron and Rautenbach about the graphs for which the Randic index attains its minimum value when k=n2. We show that the extremal graphs must have n-k vertices of degree k and k vertices of degree n-1.
Description:
Let G(k,n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randic index @g=@g(G) of a graph G is defined by: @g=@?"("u"v")(@d"u@d"v)^-^1^/^2, where @d"u is the degree of vertex u and the summation extends over all edges (uv) of G. In this paper we prove the conjecture of Delorme, Favaron and Rautenbach about the graphs for which the Randic index attains its minimum value when k=n2. We show that the extremal graphs must have n-k vertices of degree k and k vertices of degree n-1.
