Abstract:A k-ranking of a directed graph G is a labeling of the vertex set of G with k positive integers such that every directed path connecting two vertices with the same label includes a vertex with a larger label in between. The rank number of G is defined to be the smallest k such that G has a k-ranking. We find the largest possible directed graph that can be obtained from a directed path or a directed cycle by attaching new edges to the vertices such that the new graphs have the same rank number as the original g… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.