关于图的G-超幻覆盖

On the G-supermagic Coverings of Graphs

图的幻覆盖是幻方、图标号与图覆盖三个分支的完美结合.I(G,H,m)和m⊙G分别表示m个与G同构并且它们具有公共子图H的图和m个与G同构的图的点不交并组成的图.完全解决了I(G,H,m)和m⊙G的G-超幻覆盖问题.当0≤d≤5时给出了[1,mk]存在(m,d)-分拆和[1,mk+1]\{x}存在(m,0)-分拆的充要条件.

Let Gi≈ G and H be a subgraph of Gi, i ∈ [1, m]. In this paper, the Gsupermagic problems of the graph I（G, H,m） formed by taking of all the Gi＇s and identifying their subgraph H and the graph m ⊙ G formed by the vertices disjoint union of rn copies of G are completely settled. The necessary and sufficient conditions for the existence of （m, g）-partition of [1, mk] when 0 ≤d ≤ 5 and （m, 0）-partition of [1, mk＋ 1] ／ {x} are obtained.