一个五点六边图的多部图设计

G-design of Complete Multipartite Graph with G Has Five Points and Six Edges

Kn(g)是一个完全n部图,G为一个不带孤立点的简单图.一个(Kn(g),G)-设计是将Kn(g)划分成边互不相交的子图,使得每一个子图都和G同构.本文讨论了一个五点六边图G的多部图设计存在性问题,证明了(Kn(g),G)-设计存在的充要条件是n(n-1)g2≡0(mod12)且ng≥5.

Let be Kn （g） a complete multipartite graph, and G be a finite simple graph. A Kn （g） - design is a partition of the edges of Kn （g） into sub - graphs each of which is isomorphic to G . In this paper the existence of a G - design of was discussed where Kn（g） has five points and six edges and it was proved that the necessary conditions n （ n - 1 ） g^2 = 0 and ng 1〉 5 for the existence of Kn（g） - design was also sufficient.