Riv.Mat.Univ.Parma (5) 1 (1992)


A note on link diagraphs

Pages: 51-56
Received: 22 October 1991
Mathematics Subject Classification: 05C20

Abstract In this note we deal with the outlink (inlink) digraphs. The outlink (inlink) of a vertex of a digraph is the subdigraph induced by its outneighbourhood (inneighbourhood). In a digraph with constant outlink (inlink) all outlink (inlinks) are isomorphic. Then an outlink (inlink) diagraph is the constant outlink (inlink) of some diagraph. We prove that a starlike graph has at least two orientations, which are outlink (inlink) digraphs. As a corollary from the above result, we obtain the affirmative answer to Harary's question, if instars and outstars are oulink (inlink) digraphs.