Vertices Coloring Technique Using Graph Methods For Determining Minimal Map Colors

Abstract

Coloring vertices is to give color the vertices of a graph so that no two neighboring nodes are of the same colors. The minimal number of colors used to color vertices is called the graph chromatic number. The problem of coloring vertices in this study is applied on the map of the district of Sidoarjo. It is also to determine the minimal colors on the Sidoarjo region map so that the boundary between the sub-districts in Sidoarjo becomes clearer with minimal colors. In this research, First Graph is assumed to be a complete graph and Second Graph is the path, while nodes or vertices are the sub-districts and the edge of the sub-district is assumed to be neighboring sub-districts between the districts with each other. The result of the analysis shows that the join of two graphs produces a wheel graph, which has a maximum chromatic number of 4 pieces of color for the odd result and 3 pieces of color for even result. Thus, the map of the original Sidoarjo region has more than 9 colors can be given the minimum color of 4 colors can be distinguished between the district one with other district.