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Polynomials of Degree-Based Indices for Three-Dimensional Mesh Network

Ali N. A. Koam1, Ali Ahmad2, *

1 Department of Mathematics, College of Science, Jazan University, Jazan, 45142, Saudi Arabia.
2 College of Computer Science and Information Technology, Jazan University, Jazan, 45142, Saudi Arabia.

* Corresponding Author: Ali Ahmad. Email: .

Computers, Materials & Continua 2020, 65(2), 1271-1282.


In order to study the behavior and interconnection of network devices, graphs structures are used to formulate the properties in terms of mathematical models. Mesh network (meshnet) is a LAN topology in which devices are connected either directly or through some intermediate devices. These terminating and intermediate devices are considered as vertices of graph whereas wired or wireless connections among these devices are shown as edges of graph. Topological indices are used to reflect structural property of graphs in form of one real number. This structural invariant has revolutionized the field of chemistry to identify molecular descriptors of chemical compounds. These indices are extensively used for establishing relationships between the structure of nanotubes and their physico-chemical properties. In this paper a representation of sodium chloride (NaCl) is studied, because structure of NaCl is same as the Cartesian product of three paths of length exactly like a mesh network. In this way the general formula obtained in this paper can be used in chemistry as well as for any degreebased topological polynomials of three-dimensional mesh networks.


Cite This Article

A. N. A. Koam and A. Ahmad, "Polynomials of degree-based indices for three-dimensional mesh network," Computers, Materials & Continua, vol. 65, no.2, pp. 1271–1282, 2020.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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