How to find number of simple non-isomorphic graphs for a given sequence?

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Suppose a sequence of degree of vertices of a graph is given.How to find total number of graphs for the given sequence.For example if sequence (2,2,2,2,2,2) is given , then two possible graphs are - 1.Hexagon 2.Two triangles not connected to each other.So i can tell that given sequence has at least two distinct graphs. But without drawing graphs randomly , how to know total number of distinct graphs for given sequence.