Decomposition of $\lambda K_v$ into $6$-Circuits with Two Chords
Received:July 27, 2007  Revised:September 07, 2007
Key Word: graph design   holey graph design   sharply 2-transitive group.  
Fund ProjectL:the National Natural Science Foundation of China (No.10671055); the Natural Science Foundation of Hebei Province (No.A2007000230); the Foundation of Hebei Normal University (No.L2007B22).
Author NameAffiliation
KANG Qing De Institute of Mathematics, Hebei Normal University, Hebei 050016, China 
LIU Shu Xia College of Mathematics \& Stat., Hebei University of Economics and Trade, Hebei 050061, China 
YUAN Lan Dang College of Occupation Technology, Hebei Normal University, Hebei 050031, China 
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      In this paper, we discuss the $G$-decomposition of $\lambda K_v$ into $6$-circuits with two chords. We construct some holey $G$-designs using sharply 2-transitive group, and present the recursive structure by PBD. We also give a unified method to construct $G$-designs when the index equals the edge number of the discussed graph. Finally, the existence of $G$-$GD_\lambda(v)$ is given.
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