<![CDATA[A vertex coloring of a graph , is an assigments of colors to the vertices of , such that no two adjacent vertices are assigned the same color. The least number of colors needed for an vertices coloring of a graph is the chromatic number, denoted by . A graph is said to be planar if it can be drawn in the plane so that no edges crossing except at endpoints. A dual graph is constructed from the planar graph. Each region in planar graph can be represented by a vertex of the dual graph. Two vertices are connected if the region represented by these vertices are neugbours and have a common border. A diamond graph denoted by , can be used to model structure networks. In this study, it is shown that the chromatic number of dual diamond graph is χ(〖Br_n〗^* )={█(3,n=2 and n≥4@4,n=3.)┤]]>
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