Original scientific paper

https://doi.org/10.5562/cca4233

Resolving Open Problems on the Hyper-Zagreb Index and its Chemical Applications

Kinkar Chandra Das ; Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
Jayanta Bera ; Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea

Abstract

Topological indices are numerical invariants derived from molecular graphs and play an important role in characterizing chemical compounds and predicting their properties. Among the earliest descriptors are the classical Zagreb indices introduced by Gutman and Trinajstić in 1972. A more recent development is the hyper-Zagreb index (HM), defined as , where di. denotes the degree of vertex vi. In 2023, Hayat et al. posed an open problem concerning bounds on the HM index under fixed vertex-connectivity or edge-connectivity, along with the characterization of the corresponding extremal graphs. In this work, the problem is resolved by determining the extremal graphs that maximize HM index under these constraints. The investigation is further extended to several additional extremal problems, including graphs with a given number of leaves, chromatic number, and independence number. The associated extremal graphs are identified in each case. In addition, the chemical relevance of HM is examined through QSPR studies. Finally, the conclusion is presented.}

Keywords

Extremal graph; Hyper-Zagreb index; Vertex-connectivity; Edge-connectivity; QSPR analysis

Hrčak ID:

347426

URI

https://hrcak.srce.hr/347426

Publication date:

21.5.2026.

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