Balanced and strongly balanced -designs

Given a graph G , a G-decomposition of the complete graph K v is a set of graphs, all isomorphic to G , whose edge sets partition the edge set of K v . A G -decomposition of K v is also called a G-design and the graphs of the partition are said to be the blocks. A G -design is said to be balanced if the number of blocks containing any given vertex of K v is a constant. s paper the concept of strongly balanced G-design is introduced and strongly balanced path-designs are studied. Furthermore, we determine the spectrum of those path-designs which are balanced, but not strongly balanced.