Peculiar Graph Structures Construction of 4-Regular Planar Graph and Study of Odd Regions and Even Regions with Its Application

Authors

  • Atowar ul Islam Department of Computer Science and Electronics, University of Science and Technology, Meghalaya, India.
  • Sankar Haloi Department of Mathematics, Cotton University, Guwahati, Assam, India.
  • Anupam Dutta Department of Mathematics, University of Science and Technology, Meghalaya, India.

DOI:

https://doi.org/10.9734/bpi/ramrcs/v9/2633C

Keywords:

4-Regular planar graphs, sub-graphs, structure, odd regions, total regions

Abstract

Objective: Find out theorems through theoretical study of 4 -regular planar graph with odd region and even region.

In this present work we have proposed the construction of a structure of the 4-regular planar graphs for G(2m+2,4m+4) where m\(\geq\)2. Based on the proposed structure we have stated two theorems on odd regions and total regions of 4-regular planar graphs. The experimental results and proof of the stated 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.

Published

2022-03-05

How to Cite

Atowar ul Islam, Sankar Haloi, & Anupam Dutta. (2022). Peculiar Graph Structures Construction of 4-Regular Planar Graph and Study of Odd Regions and Even Regions with Its Application. Recent Advances in Mathematical Research and Computer Science Vol. 9, 114–125. https://doi.org/10.9734/bpi/ramrcs/v9/2633C

Issue

Recent Advances in Mathematical Research and Computer Science Vol. 9

Section

Chapters