Affiliations: [a] Department of Mathematical Sciences, United Arab Emirates University, Al Ain, United Arab Emirates
| [b] Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
| [c] Department of Mathematics & Statistics, Institute of Southern Punjab (ISP), Multan, Pakistan
Correspondence:
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Corresponding author. Muhammad Imran, Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates. E-mails: imrandhab@gmail.com; kamransiddiqui75@gmail.com.
Abstract: The topological descriptor are numerical parameters of a graph which characterize its topology and are usually graph invariants. Nowadays, Biological science is an energizing and quickly creating branch of knowledge together with the topological descriptor. In recent years, the investigation of living things has experienced huge extension. All the living things are composed of a fundamental unit of life called cells. The microbiology is a science that deals with the living creatures that can not be seen by naked eyes like bacteria, viruses. In recent years, eccentricity based topological indices gain a lot of importance in many disciplines like chemistry, computer science, integrated circuits, electric circuits, communication networks, biological networks. In a connected graph G, the vertex set V (G) shows the bacteria and the edge set E (G) shows the relationship between two bacterium. Mostly, the reproduction of bacteria and other microorganisms occur by binary fission process. The topological indices play a vital and useful role in indicating and analyzing physical, chemical and biological properties of any molecular graph. In this paper, we have computed eccentric polynomial and eccentric atom bond connectivity index of hyper binary trees networks (k-level) and relate these networks to biological networks. Also discuss how biological activities of these networks work in daily life.
Keywords: Biological networks, molecular structure descriptor, eccentric atom bond connectivity, eccentric connectivity polynomial, binary tree, hyper binary trees networks
