On chemical and mathematical characteristics of generalized degree–based molecular descriptors

Akbar Ali; Ivan Gutman; Boris Furtula; Abeer M. Albalahi; Amjad E. Hamza; Akbar Ali; Ivan Gutman; Boris Furtula; Abeer M. Albalahi; Amjad E. Hamza

doi:10.3934/math.2025311

AIMS Mathematics

2025, Volume 10, Issue 3: 6788-6804. doi: 10.3934/math.2025311

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On chemical and mathematical characteristics of generalized degree–based molecular descriptors

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il, Saudi Arabia
2.
Faculty of Science, University of Kragujevac, Kragujevac, Serbia

Received: 10 February 2025 Revised: 10 February 2025 Accepted: 24 March 2025 Published: 26 March 2025
MSC : 05C09, 05C92, 05C07

This paper deals with the properties of the generalized Gutman–Milovanović index, generalized elliptic–Sombor index, generalized Zagreb–Sombor index, and general Euler–Sombor index. These include, as special cases, several previously studied molecular descriptors and most of their general versions; for instance, the general Randić index, the general sum-connectivity index, the general Sombor index, etc. The aforementioned descriptors are examined for their applicability in predicting 13 properties of octane isomers, and the results are compared with the ones generated by a benchmark data set (proposed by the International Academy of Mathematical Chemistry), containing 102 descriptors of octane isomers, and also with variable and discrete Adriatic indices. Although these descriptors slightly outperform the descriptors considered for comparison in several cases, a considerable improvement is detected in the case of boiling point. Several fundamental bounds and optimal results of the above-said descriptors are also reported.
- molecular descriptor,
- topological index,
- degree of a vertex,
- degree-based topological index,
- chemical graph theory
Citation: Akbar Ali, Ivan Gutman, Boris Furtula, Abeer M. Albalahi, Amjad E. Hamza. On chemical and mathematical characteristics of generalized degree–based molecular descriptors[J]. AIMS Mathematics, 2025, 10(3): 6788-6804. doi: 10.3934/math.2025311

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Abstract

This paper deals with the properties of the generalized Gutman–Milovanović index, generalized elliptic–Sombor index, generalized Zagreb–Sombor index, and general Euler–Sombor index. These include, as special cases, several previously studied molecular descriptors and most of their general versions; for instance, the general Randić index, the general sum-connectivity index, the general Sombor index, etc. The aforementioned descriptors are examined for their applicability in predicting 13 properties of octane isomers, and the results are compared with the ones generated by a benchmark data set (proposed by the International Academy of Mathematical Chemistry), containing 102 descriptors of octane isomers, and also with variable and discrete Adriatic indices. Although these descriptors slightly outperform the descriptors considered for comparison in several cases, a considerable improvement is detected in the case of boiling point. Several fundamental bounds and optimal results of the above-said descriptors are also reported.

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