Total Coloring Schemes and Algorithms of Regular Planar Meshes

Square meshes, hexagonal meshes and honeycomb meshes are three classes of regular planar meshes, and they also are common interconnection architectures for multiprocessor systems. In this paper, we propose three optimum total coloring schemes which made these meshes have the smallest total coloring number - maximum degree plus 1. And following these total coloring schemes, we also propose three efficient algorithms for total coloring these three regular planar meshes.