Construction of different peculiar structures of 4-regular planar graph with odd regions and even regions and its application
Abstract
In this article we have proposed the construction of a structure of the 4-regular planar graphs for G(2m+2,4m+4) where m≥2. Based on the proposed structure we have specified two theorems on odd regions and total regions of 4-regular planar graphs. The experimental results and proof of the specified theorems have also been provided. Maximum region covered by odd region is also discussed using the structures of the 4-regular graph. Finally an application is given in region base map coloring and GSM network coloring.
Copyright © 2021 Atowar Ul Islam, Sankar Haloi. This 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.
Cite this article
A. U. Islam, S. Haloi, Construction of different peculiar structures of 4-regular planar graph with odd regions and even regions and its application, J. Math. Comput. Sci. 11 (2021), 2362–2376. https://doi.org/10.28919/jmcs/5494
BibTeX
@article{Islam2021,
author = {Islam, Atowar Ul and Haloi, Sankar},
title = {Construction of different peculiar structures of 4-regular planar graph with odd regions and even regions and its application},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {2362--2376},
doi = {10.28919/jmcs/5494}
}