Question

Compute the number of proper vertex coloring for the graphs below so that the number of...

Compute the number of proper vertex coloring for the graphs below so that the number of available colors is h, for h = 5 and m = 10.

(1) Star graph with 1 vertex at the center that has m neighbors.

(2) A Cycle that has m vertices, and m edges.

(3) A path that has m vertices, and m−1 edges.

(4) A wheel graph with m+1 vertices, in which a cycle graph is first formed by m vertices, and then a center vertex is added to connect to all the m vertices of the cycle.

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