  Let $G$ be a simple undirected graph. The regular number of $G$ is defined to
be the minimum number of subsets into which the edge set of $G$ can be
partitioned so that the subgraph induced by each subset is regular. In this
work, we obtain the regular number of some families of graphs and discuss some
general bounds on this parameter. Also, some of the lower or upper bounds
proved in \cite{Kulli:Janakiram:Iyer:2001} are shown here to hold with
equality.
