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

The Maximum Packing and Minimum Covering Designs for the Join Graph of K1 and C4 with a Pendent Edge