https://doi.org/10.1140/epje/s10189-025-00474-7
Regular Article - Living Systems
The sharp lower bound of tricyclic graphs with respect to the ISI index: applications in octane isomers and benzenoid hydrocarbons
1
School of Mathematics and Statistics, Suzhou University, 234000, Suzhou, Anhui, China
2
Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, 616, Nizwa, Sultanate of Oman
3
Department of Mathematical Sciences, Karakoram International University Gilgit-Baltistan, 15100, Gilgit, Pakistan
4
Department of Mechanical Engineering, College of Engineering, Qassim University, 51452, Buraydah, Saudi Arabia
5
Department of Mathematics and Statistics, Collage of Science, Collage of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
Received:
9
November
2024
Accepted:
20
January
2025
Published online:
3
February
2025
The inverse sum indeg index of a given graph G is symbolized with ISI and defined by sum of the weights 
entire links 
. We denote 
(resp. 
) the degree of a vertex u (resp. v) of G. In this paper, we obtained the sharp lower bound of tricyclic graphs with respect to the ISI index of order 
with size 
. By using atoms as vertices and chemical bonds as edges, graph theory permits the representation of molecular structures as mathematical entities called graphs. Based on the above concept, we formulated the ISI index of octane isomers (OI) and benzenoid hydrocarbons (BH) and compared the values of ISI index with various degree-based TI’s via their correlations and chemical properties. The structural analysis of octane isomers is an important application of this research, as the ISI index delivers insights into stability designs across various isomeric forms.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
