In this paper, we discuss the G-decomposition of λKv 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-GDλ（v） is given.
In this paper, we introduce the concept of the general butterfly graph B[m,n;d] for integers m,n ≥ 3, d ≥ 1, determine its balance index set, and give the necessary and sufficient condition for balanced graph B[m,n;d] to exist.
