ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

On mixed metric dimension of polycyclic aromatic hydrocarbon networks

Sunny Kumar Sharma, Vijay Kumar Bhat, Hassan Raza, and Sahil Sharma

School of Mathematics, Shri Mata Vaishno Devi University, Katra, India

E-mail: sunnysrrm94@gmail.com

Received: 15 November 2021  Accepted: 25 February 2022

Abstract:

Polycyclic aromatic hydrocarbons (PAHs) are a class of persistent organic contaminants that contain two or more aromatic rings. PAHs are commonly found in soil, water, and air, and result in mainly incomplete combustion of carbonaceous products. PAHs have a wide range of applications, such as interstellar species, optical and electrical materials, pharmaceutical industry, and other functional materials in petrochemistry. The chemical graph theory helps in understanding the complex structure of molecules. The parameters of resolvability for graph \(\Gamma =(V,E)\) are a relatively novel advanced area where the entire structure is constructed so that each vertex (atom) or/and edge (bond) represents a unique position. In this paper, we study the resolvability parameter, i.e., mixed metric dimension for the complex molecular structure of PAHs. We also prove that the mixed metric dimension is unbounded and is not constant for PAHs.

Keywords: Metric dimension; Polycyclic aromatic hydrocarbon; Mixed metric dimension; Independent set; Molecular graph; 05C12; 05C76; 05C90

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-022-02151-x

Chemical Papers 76 (7) 4115–4128 (2022)