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# Computational aspects of line graph of carbon nanocones

#### Zafar Hussain,

##### University of Lahore, PK
Department of Mathematics and Statistics

#### Mobeen Munir,

##### Department of Mathematics, University of Education, Lahore, PK
Department of Mathematics

#### Waqas Nazeer,

##### Government College University, Lahore, PK
Department of Mathematics

##### University of Okara, PK
Division of Science and Technology

#### Shin Min Kang,

##### Gyeongsang National University, Jinju, KR

Department of Mathematics and RINS

#### Young Chel Kwun

##### Dong-A University, Busan, KR
Department of Mathematics

## Abstract

Graph theory plays substantial role in mathematics, chemistry, QSAR and physical sciences. The basic layout of the graph theoretic model is a molecular structure in which vertices of the graph correspond to atoms, and edges correspond to chemical bonds. The study of this graph model provides information about the chemical structure. A line graph has many useful applications in physical chemistry. M-polynomial is rich in producing closed forms of many degree-based topological indices which correlates chemical properties of the material under investigation. This polynomial is used in computing closed formulas of many degree-based topological invariants of the molecular structures. The molecular graph of carbon nanocones has a conical structure with a cycle of length k at its core and n layers of hexagons placed at the conical surface around its centre. In this study, we transformed the molecular structure of carbon nanocones into graph theoretic model and produced its line graph. Thereafter, we determined closed formulas for M-polynomials of line graphs of nanocones. We also recovered important topological degree-based indices of the line graph of nanocones. Moreover, we provide different graphs of topological indices and their relations with the parameters of the line graph of nanocones. These graphs depict the actual dependencies of the topological indices on the parameters of the carbon nanocones.

##### Keywords: Degree-based topological index,general Randic index,line graph,M-polynomial,symmetric division index,Zagreb index
How to Cite: Hussain, Z., Munir, M., Nazeer, W., Saleem, M.S., Min Kang, S. and Chel Kwun, Y., 2020. Computational aspects of line graph of carbon nanocones. Journal of the National Science Foundation of Sri Lanka, 47(4), pp.435–443. DOI: http://doi.org/10.4038/jnsfsr.v47i4.9681
Published on 25 Jan 2020.
Peer Reviewed