On Partitional and Other Related Graphs

The partitional graphs, which are a subclass of the sequential graphs, were recently introduced by Ichishima and Oshima (Math Comput Sci 3:39–45, 2010), and the cartesian product of a partitional graph and K ₂ was shown to be partitional, sequential, harmonious and felicitous. In this paper, we present some necessary conditions for a graph to be partitional. By means of these, we study the partitional properties of certain classes of graphs. In particular, we completely characterize the classes of the graphs B _m and K _m,2 × Q _n that are partitional. We also establish the relationships between partitional graphs and graphs with strong α-valuations as well as strongly felicitous graphs.