Nonexistences of the Packing and Covering Designs for the Join Graph of K1 and C4 with a Pendent Edge

摘要

Let lKv be the complete multigraph with v vertices. A G -design G-GDl(v) of lKv is a pair (X,B), where X is the vertex set of Kv and B is a collection of subgraphs of Kv, called blocks, such that each block is isomorphic to and any two distinct vertices in G are joined in Kv exact(at most, at least) l blocks of B. In this paper, we will discuss nonexistences and constructions of the maximum packing designs and the minimum covering designs for the join graph of K1 and C4 with a pendent edge for l=1.