The Sombor index and harmonic index of chemical trees with a given number of vertices of maximum degree
Iqra Jahangirikrahjahangir@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , Memoona Ahmadmemoona.ahm@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , Sultan Ahmadraosultan58@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile → , *Rashid FarooqCorresponding authorfarook.ra@gmail.comDepartment of MathematicsSchool of Natural SciencesNational University of Sciences and TechnologyIslamabad, H-12, 44000, PakistanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 06 Jun 2024
- Published Online:
- 05 Feb 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2227
- Pages:
- 2599–2620
Abstract
For a graph G, the Sombor index and harmonic index are respectively defined as (SO(G)=∑uv∈E(G) √(degG2 (u) + degG2 (u) and H(G) = ∑uv∈E(G) 2/(degG (u) + degG(v), where E(G) is the edge set and degG (u) denoting the degree of a vertex u in G. In this paper, we aim to find extremal trees in the class of chemical trees with the given number of vertices of degree 4 for the Sombor index and the harmonic index. We observe that the extremal chemical trees maximizing the Sombor index also minimize the harmonic index in this class. Furthermore, we construct the corresponding extremal trees.
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References
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