Cayley色图中的Hamilton路

HAMILTON PATH IN CAYLEY COLOR GRAPH

Joseph B.Klerlein 在文[1]中证明了有限 Abell 群Γ具有极小生成元集△使Cayley 色图 D_△(T)为有向 Hamilton 图.本文证明了当Γ是 Abell 群时,连通的cayley 色图D_△(Γ)具有有向 Hamilton 路对任意的△成立,并举例说明一般的D_△(Γ)未必是 Hamilton 图.

Joseph B Klerlein proved that every finite abe(?)ian group Γ has a minimalgenerating set such that Cayley color graph D_△(Γ) becomes a Hamilton graph.In this paper,it is shown that the connected Cay ey color graph D_△(Γ),forevery finite abelian group Γ,has a directed Hamilton path,and we give anexample to show that in general D_△(Γ) is not a Hamilton graph.