On M -polynomial-based topological descriptors of chemical crystal structures and their applications
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On M-polynomial-based topological descriptors of chemical crystal structures and their applications Yu-Ming Chu1,2,a , Muhammad Imran3,b , Abdul Qudair Baig4,c , Shehnaz Akhter5,d , Muhammad Kamran Siddiqui6,e 1 Department of Mathematics, Huzhou University, Huzhou 313000, People’s Republic of China 2 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha
University of Science and Technology, Changsha 410114, People’s Republic of China
3 Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, United
Arab Emirates
4 Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan 5 School of Natural Sciences, National University of Sciences and Technology, Islamabad 44000, Pakistan 6 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan
Received: 16 October 2020 / Accepted: 27 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A graph in which atoms are taken as vertices and bonds among atoms can be presented by edges is recognized as a molecular graph. For such molecular graphs, we can investigate the topological descriptors and topological polynomials providing their bioactivity as well as their physio-chemical characteristics. These topological descriptors are the numerical quantities of the molecular graph that discuss its topology and are usually graph invariants. Let m ab (H) where a, b ≥ 1 be the cardinality of edges uv in H such that ( u , v ) = (a, b). M-polynomial for H can be computed by the relation M(H; z1 , z2 ) = m ab (H)za1 zb2 . a≤b
More preciously in this article, various molecular topological structure invariants of vital significance, known as first, second, modified and augmented Zagreb indices, inverse and general Randi´c indices, symmetric division, harmonic, inverse sum index and forgotten indices of chemical structures namely crystal cubic carbon CCC(n) and carbon graphite structure CG(m, n) are figured out and recovered applying general technique of topological polynomials.
1 Introduction A molecular graph consisting vertices and edges depicted by atoms and bonds, respectively, and concept of vertex-degree in a graph is same as the concept of valency in chemistry [11,29].
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] d e-mail: [email protected] e e-mail: [email protected] (corresponding author)
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In graph theory, the structural properties of graphs are being investigated with the help of topological indices. These chemicals have the broad range of implementations in numerous fields such as chemistry, drug design, pharmaceutical and in discrete dynamical systems. Also they have variety of usage in industry. The topological descriptor [9] is the numerical value which depicts some facts related to the structure of compound. Many researcher
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