Mathematical Sciences: Faculty Publications
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.
Recommended Citation
Wang, Hua.
2008.
"Extremal Trees with Given Degree Sequence for the Randić Index."
Discrete Mathematics, 308 (15): 3407-3411.
doi: 10.1016/j.disc.2007.06.026
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/714
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