In each graph, the degrees of the vertices form a sequence, which we call the degree sequence. Conversely, for every sequence d of positive integers, cannot be found a simple graph with degree sequence d. The sequence d is called graphic, where there is a simple graph G with the degree sequence d and the graph G is called a realization of d. Havel and Hakimi found and proved the necessary and sufficient condition for a sequence of numbers to be graphic. For a graphic sequence d, graph parameter ? and opt ? {min, max}, let ?opt(d) = opt{?(G) : G ? G(d)}, where G(d) is the family of graphs with degree sequence d. For every graph G, the values of ?min(d(G)) and ?max(d(G)) are the best possible lower and upper bounds on ?(G) that only depend on the degree sequence of G.