On strong distances in oriented graphs

Authors:
Peter Dankelmann;Henda C. Swart;David P. Day
Affiliations:
School of Mathematical and Statistical Sciences, University of Natal, Durban 4001, South Africa;School of Mathematical and Statistical Sciences, University of Natal, Durban 4001, South Africa;Department of Mathematics, Durban Institute of Technology, P.O. Box 953, Durban 4001, South Africa
Venue:
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Year:
2003

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Abstract

Let D be a strongly connected digraph. The strong distance between two vertices u and v in D, denoted by sdD(u,v) is the minimum size of a strongly connected subdigraph of D containing u and v. The strong eccentricity, se(u), of a vertex u of D, is the strong distance between u and a vertex farthest from u. The minimum strong eccentricity among the vertices of D is the strong radius, srad(D), and the maximum strong eccentricity is the strong diameter, sdiam(D). For asymmetric digraphs (that is, oriented graphs) we present bounds on the strong radius in terms of order and on the strong diameter in terms of order, girth and connectivity.