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Chapter 2.5, Problem 92E Step-by-step solution Step 1 of 1 Chromatic Number of a Graph Consider the chromatic number of a graph G: x(G) Since, the chromatic number is the smallest number of distinct colors needed so that to assign each vertex of the graph a color with adjacent vertices having different colors. Since, the word chromatic number is representative of the word color (derived from Greek). Therefore is aptly named as the chromatic number of the graph G.