On the Maximum ABS Index of Fixed-Order Trees with a Given Maximum Degree

被引：0

作者：

Maitreyi, Venkatesan ^{[1
]}

Elumalai, Suresh ^{[1
]}

Ali, Akbar ^{[2
]}

Balachandran, Selvaraj ^{[3
]}

Saber, Hicham ^{[2
]}

Attiya, Adel A. ^{[2
,4
]}

机构：

[1] SRM Inst Sci & Technol, Fac Engn & Technol, Coll Engn & Technol, Dept Math, Kattankulathur 603203, Tamil Nadu, India

[2] Univ Hail, Coll Sci, Dept Math, POB 2240, Hail, Saudi Arabia

[3] SASTRA Deemed Univ, Sch Arts Sci & Humanities, Dept Math, Thanjavur 613401, Tamil Nadu, India

[4] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

MATHEMATICS | 2024年 / 12卷 / 17期

关键词：

topological index; atom-bond sum-connectivity index; tree graph; maximum degree; SUM-CONNECTIVITY INDEX; EXTREMAL PROBLEMS;

D O I：

10.3390/math12172704

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The ABS (atom-bond sum-connectivity) index of a graph G is denoted by ABS(G) and is defined as & sum;xy is an element of E(G)(dx+dy)-1(dx+dy-2), where dx represents the degree of the vertex x in G. In this paper, we derive the best possible upper bounds on the ABS index for fixed-order trees possessing a given maximum degree, which provides a solution to the open problem proposed quite recently by Hussain, Liu and Hua.

引用

页数：11

共 39 条

[1] Extremal values of the atom-bond sum-connectivity index in bicyclic graphs [J].

Aarthi, Kannan ;

Elumalai, Suresh ;

Balachandran, Selvaraj ;

Mondal, Sourav .

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (06) :4269-4285

[2]

Ali A., 2023, El. J. Math., V5, P1

[3] Atom-bond sum-connectivity index [J].

Ali, Akbar ;

Furtula, Boris ;

Redzepovic, Izudin ;

Gutman, Ivan .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2022, 60 (10) :2081-2093

[4] Atom-bond connectivity index of graphs: a review over extremal results and bounds [J].

Ali, Akbar ;

Das, Kinkar Ch ;

Dimitrov, Darko ;

Furtula, Boris .

DISCRETE MATHEMATICS LETTERS, 2021, 5 :68-93

[5]

Ali A, 2019, MATCH-COMMUN MATH CO, V81, P249

[6]

[Anonymous], 1985, Chemometrics Series

[7]

Azari M., 2020, New Frontiers in Nanochemistry: Concepts, Theories, and Trends

[8]

Bondy J.A., 2008, Graph Theory

[9]

Chartrand G., 2016, Graphs and Digraphs

[10]

Devillers J., 1999, Topological Indices and Related Descriptors in QSAR and QSPR

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