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.

Can be downloaded as
postscript (338569 bytes),
PDF (172751 bytes), or
dvi (22972 bytes).

Appears in Bulletin of the Institute of Combinatorics and
its Applications, 45 (2005) 4150.

Presented at the 13th Australasian
Workshop on Combinatorial Algorithms (AWOCA)
(AWOCA),
Fraser Island, Australia. (Unfortunately, I was not able to attend!)

Mirka Miller and Joe Ryan are now faculty members at the
School of Information Technology and Mathematical Sciences,
University of Ballarat, Ballarat, Victoria 3353, Australia.
But now they are back in Newcastle.

A link to a talk (by Joe) about this paper:
conference talk.

Selected papers which refer to this one:

Nacho Lopez,
A generalization of digraph operators related to distance
properties in digraphs,
Bulletin of the Institute of Combinatorics and its Applications,
60 (2010) 4961.
Back to list of publications.