Locally Balanced G-Designs

Let G be a graph and let K(n )be the complete graph of order n. A G-design is a decomposition of the set of edges of K-n in graphs isomorphic to G, which are called blocks. It is well-known that a G-design is balanced if all the vertices are contained in the number of blocks of G. In this paper, the definition of locally balanced G-design is given, generalizing the existing concepts related to balanced designs. Further, locally balanced G-designs are studied in the cases in which G approximately equal to C-4+e and G approximately equal to C-4+P-3, determining the spectrum.