Peculiar Graph Structures Construction of 4-Regular Planar Graph and Study of Odd Regions and Even Regions with Its Application | Chapter 09 | Recent Recent Advances in Mathematical Research and Computer Science Vol. 9

 The goal is to discover theorems by conducting theoretical research on a four-regular planar graph with odd and even regions.

In this paper, we suggest constructing a structure of 4-regular planar graphs for G(2m+2,4m+4), where m≥2.  We have established two theorems on odd regions and total regions of 4-regular planar graphs based on the proposed structure. Experiment findings and proof of the aforementioned theorems are also presented. The structures of the 4-regular graph are also used to examine the maximum region covered by odd region. Finally, an application in region basis map colouring and GSM network colouring is provided.

Author(S) Details

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.

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