Packings and Coverings of $\lambda{K_v}$ with 2 Graphs of 6 Vertices and 7 Edges
Received:February 13, 2009  Revised:January 18, 2010
Key Word: $G$-design   $G$-packing design   $G$-covering design.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.10671055)
 Author Name Affiliation Yan Ke DU Institute of Applied Mathematics, Mechanical Engineering College, Hebei 050003, P. R. China Qing De KANG Institute of Mathematics, Hebei Normal University, Hebei 050016, P. R. China
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A maximum ($v,G,\lambda$)-$PD$ and a minimum ($v,G,\lambda$)-$CD$ are studied for 2 graphs of 6 vertices and 7 edges. By means of difference method" and holey graph design'', we obtain the result: there exists a $(v,G_i,\lambda)$-$OPD$ $(OCD)$ for $v\equiv 2,3,4,5,6~({\rm mod}\,~7)$, $\lambda \geq 1,~i=1,2$.