Abstract
Let G be a graph and let Kn be the complete graph of order n. A G-design is a decomposition of the set of edges of Kn 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≅C4+e and G≅C4+P3, determining the spectrum.
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