λ-packings andλ-coverings by Graphs With Six Vertices and Seven Edges
Let λkv, be the complete multigraph with vvertices and G a finite simple graph.A G-design ( G-packing design, G-covering design) ofλkv, denoted by (v, G, λ)-GD(v, G,λ)-PD, (v, G, λ)-CD), 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 G and any two distinct vertices in Kv are joined in exactly (at most, at least) λ blocks of B. A packing (covering) design is said to be maximum (minimum) if no other such packing (covering) design has more (fewer) blocks. In this paper, a maximum (v, G, λ)-PD and a minimum (v, G,λ)-CD are constructed for 3 grraphs of 6 vrertices and 7 edges.
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