General sum-connectivity index of unicyclic graphs with given diameter

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

doi:10.1016/j.dam.2021.02.012

General sum-connectivity 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

For α∈R, the general sum-connectivity index of a graph G is defined as χ_α(G)=∑_uv∈E(G)[deg_G(u)+deg_G(v)]^α, where E(G) is the edge set of G and deg_G(v) is the degree of a vertex v in G. Let U_n,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in U_n,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in U_n,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in U_n,d follow from the lower bound on the general sum-connectivity index.

Original language	English
Pages (from-to)	39-46
Number of pages	8
Journal	Discrete Applied Mathematics
Volume	295
DOIs	https://doi.org/10.1016/j.dam.2021.02.012
State	Published - 31 May 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Diameter
General sum-connectivity index
Unicyclic graphs

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.dam.2021.02.012

Cite this

@article{4e5879d59a7d4a5daf3d48095777944f,

title = "General sum-connectivity index of unicyclic graphs with given diameter",

abstract = "For α∈R, the general sum-connectivity index of a graph G is defined as χα(G)=∑uv∈E(G)[degG(u)+degG(v)]α, where E(G) is the edge set of G and degG(v) is the degree of a vertex v in G. Let Un,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in Un,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in Un,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in Un,d follow from the lower bound on the general sum-connectivity index.",

keywords = "Diameter, General sum-connectivity index, Unicyclic graphs",

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 = "2021",

month = may,

day = "31",

doi = "10.1016/j.dam.2021.02.012",

language = "English",

volume = "295",

pages = "39--46",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - General sum-connectivity index of unicyclic graphs with given diameter

AU - Alfuraidan, Monther Rashed

AU - Das, Kinkar Chandra

AU - Vetrík, Tomáš

AU - Balachandran, Selvaraj

PY - 2021/5/31

Y1 - 2021/5/31

N2 - For α∈R, the general sum-connectivity index of a graph G is defined as χα(G)=∑uv∈E(G)[degG(u)+degG(v)]α, where E(G) is the edge set of G and degG(v) is the degree of a vertex v in G. Let Un,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in Un,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in Un,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in Un,d follow from the lower bound on the general sum-connectivity index.

AB - For α∈R, the general sum-connectivity index of a graph G is defined as χα(G)=∑uv∈E(G)[degG(u)+degG(v)]α, where E(G) is the edge set of G and degG(v) is the degree of a vertex v in G. Let Un,d be the set of unicyclic graphs with n vertices and diameter d.We present the graph with the smallest general sum-connectivity index among the graphs in Un,d for −1≤α<0 and the graph with the largest general sum-connectivity index among the graphs in Un,d for 0<α<1. Sharp lower bounds on the classical sum-connectivity index and the harmonic index for graphs in Un,d follow from the lower bound on the general sum-connectivity index.

KW - Diameter

KW - General sum-connectivity index

KW - Unicyclic graphs

UR - http://www.scopus.com/inward/record.url?scp=85101535608&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2021.02.012

DO - 10.1016/j.dam.2021.02.012

M3 - Article

AN - SCOPUS:85101535608

SN - 0166-218X

VL - 295

SP - 39

EP - 46

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

General sum-connectivity index of unicyclic graphs with given diameter

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this