| Let n,A and t be positive integers. We use notation Kn(t) todenote the complete n -partite multi-graph based on vertex set X = in which X1 = X2 =Xn = t and every edge has multiplicity . Given a simple graph without isolated vertices , a ((Kn(t)),F)-design is defined to be an ordered pair ( V(Kn (t)), D ) where D is a collection of subgraphs isomorphic to F in Kn(t) such that their edges form a partition of edge-set of Kn(t). In this paper , we give the necessary and sufficient conditions of the existence of a ((Kn(t)),F)-design for any conneted graph with four vertices.Zhao TongDirected by Prof. Yin Jianxing... |
