Iterations of Eccentric Digraphs

Mirka Miller, School of Electrical Engineering and Computer Science, The University of Newcastle, NSW, Australia.
Joan Gimbert, Departament de Mathematica, Universitat de Lleida, Spain.
Frank Ruskey, Department of Computer Science, University of Victoria, Canada.
Joseph Ryan, Information Systems Group, Department of Management, The University of Newcastle, NSW, Australia.

Abstract:

The eccentricity e(u) of vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). 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 if and only if v is an eccentric vertex of u. In this paper we consider the behaviour of an iterated sequence of eccentric graphs or digraphs of a graph or a digraph. The paper concludes with several open problems.



Back to list of publications.