Extremal Trees with Given Degree Sequence for the Randić Index

Hua Wang

doi:10.1016/j.disc.2007.06.026

Extremal Trees with Given Degree Sequence for the Randić Index

Hua Wang

Mathematical Sciences

University of Florida

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

<div class="line" id="line-27"> The Randi&cacute; 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 Randi&cacute; index, thus answering the same question for weight. We also provide an algorithm to construct such trees.</div>

Original language	American English
Journal	Discrete Mathematics
Volume	308
DOIs	https://doi.org/10.1016/j.disc.2007.06.026
State	Published - Aug 6 2008

Disciplines

Mathematics

Keywords

Degree sequence
Randić index
Weight

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10.1016/j.disc.2007.06.026License: Unspecified

Cite this

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title = "Extremal Trees with Given Degree Sequence for the Randi{\'c} Index",

abstract = " The Randi&cacute; 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 Randi&cacute; index, thus answering the same question for weight. We also provide an algorithm to construct such trees.",

keywords = "Degree sequence, Randi{\'c} index, Weight",

author = "Hua Wang",

year = "2008",

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day = "6",

doi = "10.1016/j.disc.2007.06.026",

language = "American English",

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journal = "Discrete Mathematics",

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N2 - The Randi&cacute; 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 Randi&cacute; index, thus answering the same question for weight. We also provide an algorithm to construct such trees.

AB - The Randi&cacute; 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 Randi&cacute; index, thus answering the same question for weight. We also provide an algorithm to construct such trees.

KW - Degree sequence

KW - Randić index

KW - Weight

UR - https://doi.org/10.1016/j.disc.2007.06.026

U2 - 10.1016/j.disc.2007.06.026

DO - 10.1016/j.disc.2007.06.026

M3 - Article

SN - 0012-365X

VL - 308

JO - Discrete Mathematics

JF - Discrete Mathematics

ER -

Extremal Trees with Given Degree Sequence for the Randić Index

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