Title

Extremal Trees with Given Degree Sequence for the Randić Index

Document Type

Article

Publication Date

8-6-2008

Publication Title

Discrete Mathematics

DOI

10.1016/j.disc.2007.06.026

ISSN

0012-365X

Abstract

The Randić index of a graph G is the sum of ((d(u))(d(v)))α over all edges uv of G, where d(v) denotes the degree of v in G, α≠0. When α=1, it is the weight of a graph. Delorme, Favaron, and Rautenbach characterized the trees with a given degree sequence with maximum weight, where the question of finding the tree that minimizes the weight is left open. In this note, we characterize the extremal trees with given degree sequence for the Randić index, thus answering the same question for weight. We also provide an algorithm to construct such trees.

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