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 Chartrand1
, John Frederick Fink2
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
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.