PACKINGS OF THE COMPLETE DIRECTED GRAPH WITH m-CIRCUITS

A packing of the complete directed symmetric graph DKv with m-circuits, denoted by(v,m)-DCP, is defined to he a family of are-disjoint m-circuits of DK, such that any one arc of DKv occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m-circults in such a packing. The packing problem is to determine the value P(v,m) for everyinteger v ≥ m. In this paper, the problem is reduced to the case m 6 ≤v≤2m-[(4m-3的平方极) 1/2]，for any fixed even integer m≥4，In particular,the values of P（v,m） are completely determined for m=12,14 and 16.     

积图Pm×C4n的k-优美性

Let k be a positive integer. The simple graph G=(V, E) is called k-graceful if there exists a injection.