One Variety Conjectures of Complete-transposition Network
Hou Fei-fei · 2012
Complete-transposition Networks are important cayley graphs model in networks design.One variety conjectures of complete-transposition networks were proposed as follows:for any intger n≥3,if n=0(mod 4) or 1(mod 4),CTn is a union of k(1≤k≤n(n-1) 4) edge-disjoint Hamiltonian cycles and n(n-1) 2-2k perfect matchings.if n=2(mod 4) or 3(mod 4),CTn is a union of k(1≤k≤n(n-1)-2 4) edge-disjoint Hamiltonian cycles and n(n-1) 2-2k perfect matchings.We proved the conjectures are true for n=3,4,and n=5(1≤k≤4),n=6(1≤k≤6).