Explicit Formulas of Partitions of Stable Sets of the Direct Product on Several Pairs of Complementary Graphs

In this paper, the main problem is counting of partitions of stable sets of the direct product on several pairs of complementary graphs. Counting of stable set partitions is NP-hard problem. It is difficult the same as counting of crossing number.By means of counting theory of S(n) -factors and two counting formulas of partitions of stable sets of the direct product graphs, the author obtains explicit formulas of the direct product on several pairs of complementary graphs, such as the wheel graph,the product of (n-2)-regular graph,etc, and discovers these explicit formulas related to Fibonacci number, Lucas number, Stirling number and Bell number. So that these combinatorial numbers are given graphic interpretations.Further, the product of n continuous Fibonacci numbersF1F2...Fn and the product of n continous Bellnumbers b(1)b(2)...b(n) are given graphic interpretations. Finally, a counter example of the formula for calculating the sum of stable set partitions is presented.The author achieves some advances in its field.For combinatorics and graph theory, it is of reference value and significant.