Publication Type : Journal Article
Publisher : Indian Journal of Mathematics
Source : Indian Journal of Mathematics, Volume 51, Issue 3, Number 3, p.597–609 (2009)
Url : http://arxiv.org/abs/1001.4213
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Year : 2009
Abstract : Abstract: In a digraph $ D=(X, mathcal {U}) $, not necessarily finite, an arc $(x, y) in mathcal {U} $ is reachable from a vertex $ u $ if there exists a directed walk $ W $ that originates from $ u $ and contains $(x, y) $. A subset $ S subseteq X $ is an arc-reaching set of $ D $ if for every arc $(x, y) $ there exists a diwalk $ W $ originating at a vertex $ u in S $ and containing $(x, y) $. A minimal arc-reaching set is an arc-basis. $ S $ is a point-reaching set if for every vertex $ v $ there exists a diwalk $ W $ to $ v $ riginating at a vertex $ u in S $
Cite this Research Publication : B. D. Acharya, Germina, K. A., Abhishek, K., Rao, S. B., and Zaslavsky, T., “Point-and arc-reaching sets of vertices in a digraph”, Indian Journal of Mathematics, vol. 51, no. 3, pp. 597–609, 2009.