Journal of Prime Research in Mathematics

# Sombor index of some nanostructures

Ammar Alsinai$$^a$$, B. Basavanagoud$$^{b,*}$$, Mahammadsadiq Sayyed$$^b$$, Mohammad Reza Farahani$$^c$$
$$^a$$Department of Studies in Mathematics, University of Mysore, Manasagangotri Mysuru-570006, India.
$$^b$$ Department of Mathematics, Karnatak University, Dharwad-580003, Karnataka, India.
$$^c$$ Department of Mathematics, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Iran.
Correspondence should be addressed to: B. Basavanagoud at b.basavanagoud@gmail.com

### Abstract

Topological indices are extensively used for establishing relationship between the nanostructure and their physico-chemical properties. The invention of new nanostructures gives a key note to industry, electronics, pharmaceutical, medical treatments, communication, information and food science and so on. In this paper, Sombor index is tested with physico-chemical properties of octane isomers such as entropy, acentric factor, enthalpy of vaporization (HVAP) and standard enthalpy of vaporization (DHVAP) using the linear models. The Sombor index shows excellent correlation with these chemical properties. Specially, high correlation with DHVAP (coefficient of correlation 0.9392673). Further, we obtain Sombor index of 2D-lattice, nanotube and nanotorus of $$TUC_{4}C_{8}[p,q]$$ and subdivision graph of 2D-lattice, nanotube and nanotorus of $$TUC_{4}C_{8}[p,q]$$.

#### Keywords:

Sombor index, nanostructure and subdivision graph.