This research aims to construct a dual graph from a wheel graph (Wn*) and determine the dual graph chromatic number of the wheel graph (Wn*). This research starts from describing some wheel graph from to , then construct a dual graph from a wheel graph from to , then gives color to the vertices of the dual graph by determining the chromatic number. The result showed that the wheel graph is a self-dual graph because it is isomorphic with its dual graph, namely . The vertex coloring is obtained by determining the chromatic number of the dual graph of the wheel graph, determining the pattern of the chromatic number and giving the color. Based on the research results, the chromatic number of vertex coloring on dual graph of a wheel graph is:
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