ABC Index of Trees with Fixed Number of Leaves

被引：0

作者：

Goubko, Mikhail ^{[1
]}

Magnant, Colton ^{[2
]}

Nowbandegani, Pouria Salehi ^{[2
]}

Gutman, Ivan ^{[3
,4
]}

机构：

[1] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow, Russia

[2] Georgia So Univ, Dept Math Sci, Statesboro, GA 30460 USA

[3] Univ Kragujevac, Fac Sci, Kragujevac 34000, Serbia

[4] State Univ Novi Pazar, Novi Pazar, Serbia

来源：

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY | 2015年 / 74卷 / 03期

关键词：

TOPOLOGICAL INDEXES;

D O I：

暂无

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

Given a graph G, the atom-bond connectivity (ABC) index is defined to be ABC(G) = Sigma Euv is an element of E(G)root d(G)(u)+d(G)(v)-2/d(G)(u)d(G)(v), where E(G) is the edge set of graph G and d(G)(v) is the degree of vertex v in graph G. The paper [10] claims to classify tho trees with a fixed number of leaves which minimize the ABC index. Unfortunately, there is a gap in the proof, leading to other examples that contradict the main result of that work. These examples and the problem are discussed in this note.

引用

下载

页码：697 / 702

页数：6

共 50 条

[1] On Trees with Minimal ABC Index among Trees with Given Number of Leaves
Lin, Wenshui
Chen, Jiwen
Ma, Chi
Zhang, Yuan
Chen, Junjie
Zhang, Dongzhan
Jia, Fei
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2016, 76 (01) : 131 - 140
[2] On bond incident degree index of chemical trees with a fixed order and a fixed number of leaves
Du, Jianwei
Sun, Xiaoling
APPLIED MATHEMATICS AND COMPUTATION, 2024, 464
[3] On the minimal ABC index of trees with k leaves
Lin, Wenshui
Li, Peixi
Chen, Jianfeng
Ma, Chi
Zhang, Yuan
Zhang, Dongzhan
DISCRETE APPLIED MATHEMATICS, 2017, 217 : 622 - 627
[4] The Structure of ABC-Minimal Trees with Given Number of Leaves
Mohar, Bojan
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2018, 79 (02) : 415 - 430
[5] On Sombor index of trees with fixed domination number
Sun, Xiaoling
Du, Jianwei
APPLIED MATHEMATICS AND COMPUTATION, 2022, 421
[6] Which tree has the smallest ABC index among trees with k leaves?
Magnant, Colton
Nowbandegani, Pouria Salehi
Gutman, Ivan
DISCRETE APPLIED MATHEMATICS, 2015, 194 : 143 - 146
[7] ON MULTIPLICATIVE SUM ZAGREB INDEX OF TREES WITH FIXED DOMINATION NUMBER
Sun, Xiaoling
Gao, Yubin
Du, Jianwei
JOURNAL OF MATHEMATICAL INEQUALITIES, 2023, 17 (01): : 83 - 98
[8] Minimum Randic Index of Trees with Fixed Total Domination Number
Jamri, Ayu Ameliatul Shahilah Ahmad
Movahedi, Fateme
Hasni, Roslan
Gobithaasan, Rudrusamy
Akhbari, Mohammad Hadi
MATHEMATICS, 2022, 10 (20)
[9] Maximum atom-bond sum-connectivity index of n-order trees with fixed number of leaves
Noureen, Sadia
Ali, Akbar
DISCRETE MATHEMATICS LETTERS, 2023, 12 : 26 - 28
[10] On the Wiener polarity index of trees with maximum degree or given number of leaves
Liu, Bolian
Hou, Huoquan
Huang, Yufei
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (07) : 2053 - 2057

← 1 2 3 4 5 →