Extremal chemical trees with given number of vertices of maximum degree for degree-based topological indices

Ahmad, Memoona; Jahangir, Iqra; Ahmad, Sultan; Farooq, Rashid

doi:10.47974/JDMSC-2305

Open Access Research Article

Extremal chemical trees with given number of vertices of maximum degree for degree-based topological indices

Memoona Ahmadmemoona.ahm@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , Iqra Jahangirikrahjahangir@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , ^*Sultan AhmadCorresponding authorraosultan58@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , Rashid Farooqfarook.ra@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile →

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pp. 1–18Online FirstApril 2026DOI: 10.47974/JDMSC-2305 Crossmark XML

Received:: 02 Sep 2024
Published Online:: 01 Apr 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2305
Pages:: 1–18

Abstract

We define the general sum index for a graph G as follows: GSl,γ (G) = ∑ab∈E(G)‍ γ (dG (a)2/γ + dG (b)2/γ)l where dG(a) is the degree of a vertex a and, l and γ are non-zero real numbers. In this paper, we consider a class 𝒞𝒯(n, k) of chemical trees with given order n and k vertices of maximum degree. We find those graphs in 𝒞𝒯(n, k) which has extremal values of 𝒞𝒯l,γ when [γ = 1, –1/2 ≤ l < 0] or [γ = 2, –1 ≤ l < 0] or [γ ∈{1, 2} and 0 < l ≤ 1/2]. Given different values of l and γ within the mentioned brackets, the GSl,γ coincides with the Sombor index (SO), modified Sombor index (SOm), general sum-connectivity index (Xl) and harmonic index (H). Furthermore, our findings reveal that in the class 𝒞 𝒯 (n, k), specific chemical trees with maximum values of SOm, H and Xl (–1 ≤ l < 0) simultaneously attain minimum values of SO and Xl (0 < l ≤ 1/2).

Keywords

General sum index Sombor index Modified Sombor index Harmonic index General sum-connectivity index Chemical trees

Subject Classifications

05C0905C3505C92

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