Graph Designs of Fourvertex Conneted Graphs 

Author  ZhaoTong 
Tutor  YinJianXing 
School  Suzhou University 
Course  Applied Mathematics 
Keywords  The complete npartite multigraph graph design existence 
CLC  O157.5 
Type  Master's thesis 
Year  2002 
Downloads  25 
Quotes  5 
Let n,A and t be positive integers. We use notation Kn(t) todenote the complete n partite multigraph 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 edgeset 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