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.
|Titolo:||Balanced and Strongly Balanced Pk-designs|
|Data di pubblicazione:||2012|
|Appare nelle tipologie:||1.1 Articolo in rivista|