Balanced and Strongly Balanced Pk-designs

Given a graph G, a G-decomposition of the complete graph Kv is a set of graphs, all isomorphic to G, whose edge sets partition the edge set of Kv . A G-decomposition of Kv 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 Kv is a constant. In this paper the concept of strongly balanced G-design is introduced and strongly balanced path-designs are studied. Furthermore, we determine the spectrum of those pathdesigns which are balanced, but not strongly balanced.