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

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

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