Eccentric Digraphs
Document Type
Conference Proceeding
Publication Date
9-6-2004
Description
The distance d(u,v) from vertex u to vertex v in a digraph G is the length of the shortest directed path from u to v. The eccentricity e(v) of vertex v is the maximum distance of v to any other vertex of G. A vertex u is an eccentric vertex of vertex v if the distance from v to u is equal to the eccentricity of v. The eccentric digraph ED(G) of a digraph G is the digraph that has the same vertex set as G and the arc set defined by: there is an arc from u to v iff v is an eccentric vertex of u. The idea of the eccentric digraph of a graph was introduced by Buckley (Congr. Numer. 149 (2001) 65) and the idea of the eccentric digraph of a digraph by Boland and Miller (Proceedings of AWOCA'01, July 2001, p. 66). In this paper, we examine eccentric digraphs of digraphs for various families of digraphs and we consider the behaviour of an iterated sequence of eccentric digraphs of a digraph. The paper concludes with several open problems.
Citation Information
Boland, James; Buckley, Fred; and Miller, Mirka. 2004. Eccentric Digraphs. Discrete Mathematics. Vol.286(1-2). 25-29. https://doi.org/10.1016/j.disc.2003.11.041 ISSN: 0012-365X