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.