Judgment of Simple Graph and Degree Sequence and Its Realization through Computers

This paper deals with the positive integer sequences by the method of distributing degrees-dealing the vertices.It is possible to judge if the given integer sequences are simple graphic and degree sequences. This paper presents the concept of sub-simple graphic sequence and therefore puts forward the necessary and sufficient condition for the integer sequence A_n to be simple graphic sequence: when and only when A_n is sub-sequence of simple graph and its A~(n-2)_(2) is a sequence of a graph and the graph is a simple graph.