Counting formulas N[(X_1,X_2,…,X_i),k] of complete i-partite graphs
Nian Si-hong · Dalian Ligong Daxue xuebao · 2007
By using convolution formulas,counting problems of S(n)-factors are studied.The counting formula of S(n)-factors exactly with 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.