General Randić index of unicyclic graphs with given diameter

Monther Rashed Alfuraidan; Kinkar Chandra Das; Tomáš Vetrík; Selvaraj Balachandran

doi:10.1016/j.dam.2021.09.016

General Randić index of unicyclic graphs with given diameter

Monther Rashed Alfuraidan, Kinkar Chandra Das, Tomáš Vetrík^*, Selvaraj Balachandran

^*Corresponding author for this work

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

9 Scopus citations

Abstract

We study the general Randić index R_a(G)=∑_uv∈E(G)[deg_G(u)deg_G(v)]^a, where a∈R, E(G) is the edge set of a graph G, and deg_G(u) and deg_G(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randić index, where −0.64≤a<0. Since [Formula presented] is the Randić index of a graph G, our result holds also for the classical Randić index.

Original language	English
Pages (from-to)	7-16
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	306
DOIs	https://doi.org/10.1016/j.dam.2021.09.016
State	Published - 15 Jan 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Diameter
General Randić index
Unicyclic graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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title = "General Randi{\'c} index of unicyclic graphs with given diameter",

abstract = "We study the general Randi{\'c} index Ra(G)=∑uv∈E(G)[degG(u)degG(v)]a, where a∈R, E(G) is the edge set of a graph G, and degG(u) and degG(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randi{\'c} index, where −0.64≤a<0. Since [Formula presented] is the Randi{\'c} index of a graph G, our result holds also for the classical Randi{\'c} index.",

keywords = "Diameter, General Randi{\'c} index, Unicyclic graph",

author = "Alfuraidan, {Monther Rashed} and Das, {Kinkar Chandra} and Tom{\'a}{\v s} Vetr{\'i}k and Selvaraj Balachandran",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

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day = "15",

doi = "10.1016/j.dam.2021.09.016",

language = "English",

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T1 - General Randić index of unicyclic graphs with given diameter

AU - Alfuraidan, Monther Rashed

AU - Das, Kinkar Chandra

AU - Vetrík, Tomáš

AU - Balachandran, Selvaraj

PY - 2022/1/15

Y1 - 2022/1/15

N2 - We study the general Randić index Ra(G)=∑uv∈E(G)[degG(u)degG(v)]a, where a∈R, E(G) is the edge set of a graph G, and degG(u) and degG(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randić index, where −0.64≤a<0. Since [Formula presented] is the Randić index of a graph G, our result holds also for the classical Randić index.

AB - We study the general Randić index Ra(G)=∑uv∈E(G)[degG(u)degG(v)]a, where a∈R, E(G) is the edge set of a graph G, and degG(u) and degG(v) are the degrees of vertices u and v, respectively. For a set of unicyclic graphs of given order and diameter, we present the unique graph having the minimum general Randić index, where −0.64≤a<0. Since [Formula presented] is the Randić index of a graph G, our result holds also for the classical Randić index.

KW - Diameter

KW - General Randić index

KW - Unicyclic graph

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DO - 10.1016/j.dam.2021.09.016

M3 - Article

AN - SCOPUS:85116505286

SN - 0166-218X

VL - 306

SP - 7

EP - 16

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

General Randić index of unicyclic graphs with given diameter

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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