Maximum tree and maximum value for the randić index R-1 of trees of order n ≤ 102

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)119-136
Journal / PublicationMatch
Volume55
Issue number1
Publication statusPublished - 2006

Abstract

The Randić index R-1(G) of a graph G is defined as the sum of the weights (d(u)d(v))-1 of all edges uv of G, where d(u) denotes the degree of a vertex u in G. Trees with maximum Randić index R-1 need not be unique. Clark et al. gave the maximum values for the index of trees of order n ≤ 20. In this paper, we determine the maximum value for the Randić index R-1 of all trees of order n ≤ 102, and give one of the trees with maximum value of the index. This not only largely extends the known range of the orders n of trees with maximum index, but also gives a convincible solution for the induction initial of our previous paper. Because there is a huge number of trees of order n ≤ 102, it is not possible to directly search the trees with maximum index by a computer. Our method is to first figure out the simple structure of one of the trees of order n with maximum R-1 for each n ≤ 102, i.e., the branching subtree must be a star. Then from this simple structure, we can employ mathematical programming to easily calculate the maximum value of R-1 for each n.

Citation Format(s)

Maximum tree and maximum value for the randić index R-1 of trees of order n ≤ 102. / Hu, Yumei; Jin, Yinglie; Li, Xueliang et al.
In: Match, Vol. 55, No. 1, 2006, p. 119-136.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review