完全i部图N[(X_1,X_2,…,X_i),k]计数公式  

Counting formulas N[(X_1,X_2,…,X_i),k] of complete i-partite graphs

作　　者：杨利民[1] 王天明[1] 年四洪[1] 

机构地区：[1]大连理工大学应用数学系

出　　处：《大连理工大学学报》2007年第6期925-930,共6页Journal of Dalian University of Technology

摘　　要：采用组合卷积公式方法,研究图的S(n)-因子的计数问题.首先获得完全2-部图的恰有k个分支的S(n)-因子的计数公式,并用同样方法获得完全i-部图的恰有k个分支的S(n)-因子的计数公式,从而给出完全i-部图的所有因子数计数公式.进一步研究了完全i-部图的组合恒等式,并通过组合计算技巧,获得了完全i-部图、完全2-部图和完全3-部图的组合恒等式.该研究对图论及组合学具有理论和应用价值.By using convolution formulas, counting formula of S^（n）-factors exactly with counting problems of S^（n）-factors are studied. The k components of complete 2-partite graphs is obtained. By the same way, the counting formula of S^（n）-factors exactly with k components of complete i-partite graphs is obtained. Furthermore, the counting formula of all S^（n）-factors exactly with k components of complete i-partite graphs is obtained. Also the combinatorial identities on complete i-partite graphs are researched, and the new methods from combinatorial methods is adopted. Finally, a number of combinatorial identities of complete i-partite graphs, complete 2-partite graphs, complete 3-partite graphs are presented. The results are valuable for combinatorics and graph theory.

关 键 词：完全i部图 卷积公式 第一类STIRLING数 因子 

分 类 号：O157.5[理学—数学] O157.1[理学—基础数学]