Research Article Chemical Applicability of Newly Introduced Topological Invariants and Their Relation with Polycyclic Compounds Dilshad Alghazzawi , 1 Ali Raza , 2 Usama Munir , 3 and Md. Shajib Ali 4 1 Department of Mathematics, King Abdulaziz University, Rabigh, Saudi Arabia 2 Department of Mathematics, University of the Punjab, Lahore, Pakistan 3 Department of Mathematics, University of Education Lahore, Lahore, Pakistan 4 Department of Mathematics, Islamic University, Kushtia 7003, Bangladesh Correspondence should be addressed to Md. Shajib Ali; shajib_301@yahoo.co.in Received 2 May 2022; Revised 27 May 2022; Accepted 2 June 2022; Published 31 July 2022 Academic Editor: A. Ghareeb Copyright © 2022 Dilshad Alghazzawi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nano- chemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic GHI, harmonic-geometric (HGI), neighborhood harmonic-geometric (NHGI), and neighborhood geometric-harmonic (NGHI) indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically. 1. Introduction and Preliminaries To reduce the consumption of time and cost during ex- amining the biological, physical, and chemical properties of millions of newly invented nanomaterials, crystalline ma- terials, and drugs, chemists study the quantitative structure- property relationship (QSPR) and the quantitative structure- activity relationship (QSAR) [1–4]. Topological indices (TIs), numeric invariants describing properties of particular molecular structures, are used as a fundamental tool in the QSPR and QSAR. ese indices help in production of different chemicals with desired characteristics and esti- mation of physiochemical properties of existing compounds [5–9]. Another dominant benefit of the TIs is their effec- tiveness during investigation of different aspects of chemical compounds and new drugs, which is the fundamental re- quirement of the medical sciences and industry. Conse- quently, studying and computing the behavior of the TIs of the molecular structures is a significant source to provide qualitative and quantitative information and therefore is one of the trends in modern research. Along with drug design, isomer discrimination, chemical documentation, and bio- logical characterization, different applications of TIs in mathematical chemistry are described in [10–15]. Silicon carbides, which occur as incredibly abundant minerals in nature containing covalent bonds between carbon and silicon atoms, are biatomic compounds with tetrahedrally oriented layers of carbon and silicon atoms. Because of these strongly packed layers and short-length covalent bonds, SiC as consequences of nonoxidizing be- havior, high melting points, high erosion resistance, thermal, and chemical stability, silicon carbides have vital industrial applications [16–18]. ese electrical properties and low- cost production methodologies give superiority to silicon carbides among other metals and semiconductors. Being one of the most extensively used wide bandgap materials, SiC performs a vital role in power industries by setting new principles in power savings as rectifiers or switches in the system for data centers, wind turbines, solar cells, and electric vehicles along with high radiation and temperature- Hindawi Journal of Mathematics Volume 2022, Article ID 5867040, 16 pages https://doi.org/10.1155/2022/5867040