Ghani MU, Campena FJH, Maqbool MK, Liu JB, Dehraj S, Cancan M, Alharbi FM. Entropy Related to
K-Banhatti Indices via Valency Based on the Presence of
C6H6 in Various Molecules.
MOLECULES (BASEL, SWITZERLAND) 2023;
28:molecules28010452. [PMID:
36615642 PMCID:
PMC9824825 DOI:
10.3390/molecules28010452]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/18/2022] [Accepted: 12/19/2022] [Indexed: 01/05/2023]
Abstract
Entropy is a measure of a system's molecular disorder or unpredictability since work is produced by organized molecular motion. Shannon's entropy metric is applied to represent a random graph's variability. Entropy is a thermodynamic function in physics that, based on the variety of possible configurations for molecules to take, describes the randomness and disorder of molecules in a given system or process. Numerous issues in the fields of mathematics, biology, chemical graph theory, organic and inorganic chemistry, and other disciplines are resolved using distance-based entropy. These applications cover quantifying molecules' chemical and electrical structures, signal processing, structural investigations on crystals, and molecular ensembles. In this paper, we look at K-Banhatti entropies using K-Banhatti indices for C6H6 embedded in different chemical networks. Our goal is to investigate the valency-based molecular invariants and K-Banhatti entropies for three chemical networks: the circumnaphthalene (CNBn), the honeycomb (HBn), and the pyrene (PYn). In order to reach conclusions, we apply the method of atom-bond partitioning based on valences, which is an application of spectral graph theory. We obtain the precise values of the first K-Banhatti entropy, the second K-Banhatti entropy, the first hyper K-Banhatti entropy, and the second hyper K-Banhatti entropy for the three chemical networks in the main results and conclusion.
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