On oriented l(p,1)-labeling
Communications in Computer and Information Science
An oriented graph is a directed graph without any directed cycle of length at most 2. In this article, we characterize the oriented L(p, 1)-labeling span (Formula presented) of an oriented graph G using graph homomorphisms. Using this characterization and probabilistic techniques we prove the upper bound of (Formula presented), where Gδ is the family of graphs with maximum degree at most δ. Moreover, by proving a lower bound exponential in δ for the same graph family we conclude that the upper bound is not too far from being optimal. We also settle an open problem given by Sen (DMGT 2014) for the family of outerplanar graphs O by showing (Formula presented).
Das, Sandip; Nandi, Soumen; and Sen, Sagnik, "On oriented l(p,1)-labeling" (2018). Conference Articles. 172.