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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