On tricyclic graphs with maximum atom–bond sum–connectivity index

Sadia Noureen; Rimsha Batool; Abeer M. Albalahi; Yilun Shang; Tariq Alraqad; Akbar Ali

doi:10.1016/j.heliyon.2024.e33841

On tricyclic graphs with maximum atom–bond sum–connectivity index

Sadia Noureen, Rimsha Batool, Abeer M. Albalahi, Yilun Shang^*, Tariq Alraqad, Akbar Ali^*

^*Corresponding author for this work

Computer and Information Sciences Department

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

3 Citations (Scopus)

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Abstract

The sum-connectivity, Randić, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees. The ABS (atom-bond sum-connectivity) index is a variant of all the aforementioned three indices, which was recently put forward. Let T(n) be the class of all connected tricyclic graphs of order n. Recently, the problem of determining graphs from T(n) having the least possible value of the ABS index was solved in (Zuo et al., 2024 [39]) for the case when the maximum degree of the considered graphs does not exceed 4. The present paper addresses the problem of finding graphs from T(n) having the largest possible value of the ABS index for n≥5.

Original language	English
Article number	e33841
Pages (from-to)	1-10
Number of pages	10
Journal	Heliyon
Volume	10
Issue number	14
Early online date	3 Jul 2024
DOIs	https://doi.org/10.1016/j.heliyon.2024.e33841
Publication status	Published - 30 Jul 2024

Keywords

Atom-bond sum-connectivity index
Extremal graph theory
Topological index
Tricyclic graphs

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10.1016/j.heliyon.2024.e33841Licence: CC BY-NC

1-s2.0-S2405844024098724-mainFinal published version, 416 KBLicence: CC BY-NC

Cite this

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title = "On tricyclic graphs with maximum atom–bond sum–connectivity index",

abstract = "The sum-connectivity, Randi{\'c}, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees. The ABS (atom-bond sum-connectivity) index is a variant of all the aforementioned three indices, which was recently put forward. Let T(n) be the class of all connected tricyclic graphs of order n. Recently, the problem of determining graphs from T(n) having the least possible value of the ABS index was solved in (Zuo et al., 2024 [39]) for the case when the maximum degree of the considered graphs does not exceed 4. The present paper addresses the problem of finding graphs from T(n) having the largest possible value of the ABS index for n≥5.",

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AU - Noureen, Sadia

AU - Batool, Rimsha

AU - Albalahi, Abeer M.

AU - Shang, Yilun

AU - Alraqad, Tariq

AU - Ali, Akbar

PY - 2024/7/30

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On tricyclic graphs with maximum atom–bond sum–connectivity index

Abstract

Keywords

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