International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 36, Pages 2265-2275
doi:10.1155/S0161171203210577

The hull number of an oriented graph

Gary Chartrand,1 John Frederick Fink,2 and Ping Zhang1

1Department of Mathematics, Western Michigan University, Kalamazoo 49008, MI, USA
2Department of Mathematics, The University of Michigan-Dearborn, Dearborn 48128-1491, MI, USA

Received 27 October 2002

Copyright © 2003 Gary Chartrand et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present characterizations of connected graphs G of order n≥2 for which h+(G)=n. It is shown that for every two integers n and m with 1≤n−1≤m≤(n2), there exists a connected graph G of order n and size m such that for each integer k with 2≤k≤n, there exists an orientation of G with hull number G.