Peculiar Graph Structures Construction of 4-Regular Planar Graph and Study of Odd Regions and Even Regions with Its Application - Atowar ul Islam; Sankar Haloi; Anupam Dutta (Recent Advances in Mathematical Research and Computer Science Vol. 9, 2022)
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\(≥\)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.