Edge Coloring and Region Coloring of Planar Graphs Based on Prim’s and Kruskal’s Strategies

Abstract

Since the development of graph theory, its applications are gaining a lot of importance among the researchers. The coloring of graphs is one of those applications used for creating maps and networks. Coloring involves the use of different colors to print the regions of the graphs. A number of algorithms 7-9 have been developed for coloring the graphs. The authors 10 have already developed algorithms for coloring the vertices of the planar graphs. In this paper, we are discussing two algorithms that we have developed for coloring the edges and region to find the chromatic number of the planar graphs. Notations E(G) : {E1 , E2 , E3 , ..., En } is the set of all edges. Ei(di) : {E1(d1), E2(d2), E3(d3), ..., En(dn)}, set of edges with degree associated. R(G) : {R1 , R2 , R3 , ..., Rn } is the set of all regions. RC : Set of colored edges. C : Set of colors. P : Chromatic number (minimum number of colors used for coloring).