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Volume 14
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Article

Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules

by
Zhenhua Su
1 and
Zikai Tang
2,*
1
School of Mathematics and Computational Sciences, Huaihua University, Huaihua 418000, China
2
College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(4), 249; https://doi.org/10.3390/axioms14040249
Submission received: 12 February 2025 / Revised: 11 March 2025 / Accepted: 25 March 2025 / Published: 26 March 2025
(This article belongs to the Special Issue Advances in Combinatorial Optimization and Discrete Mathematics with Applications)
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Abstract

With geometric significance, the Euler Sombor index of a graph Γ is defined as EP(Γ)=∑{uv}∈E(Γ)d(u)2+d(v)2+d(u)d(v). It originates from the mathematical distance property and has been proven to have good chemical applications in octane isomers. In this paper, the minimum and maximum of the Euler Sombor index for unicyclic graphs with given girth, as well as the corresponding extremal graphs, are determined. As an application, the experimental values of this index for some benzenoid hydrocarbons and drug molecules were compared with the boiling point. Through regression analysis, it was further demonstrated that the Euler Sombor index has excellent predictability in the physicochemical properties of compounds.
Keywords: extreme value; Euler Sombor index; benzenoid hydrocarbons; chemical applications extreme value; Euler Sombor index; benzenoid hydrocarbons; chemical applications

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MDPI and ACS Style

Su, Z.; Tang, Z. Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules. Axioms 2025, 14, 249. https://doi.org/10.3390/axioms14040249

AMA Style

Su Z, Tang Z. Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules. Axioms. 2025; 14(4):249. https://doi.org/10.3390/axioms14040249

Chicago/Turabian Style

Su, Zhenhua, and Zikai Tang. 2025. "Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules" Axioms 14, no. 4: 249. https://doi.org/10.3390/axioms14040249

APA Style

Su, Z., & Tang, Z. (2025). Extremal Unicyclic Graphs for the Euler Sombor Index: Applications to Benzenoid Hydrocarbons and Drug Molecules. Axioms, 14(4), 249. https://doi.org/10.3390/axioms14040249

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