Bondage Number in Oriented Graphs

Erfang Shan1, Liying Kang1
1Department of Mathematics, Shanghai University, Shanghai 200436, P.R. China

Abstract

The bondage number \(b(D)\) of a digraph \(D\) is the cardinality of a smallest set of arcs whose removal from \(D\) results in a digraph with domination number greater than the domination number of \(D\). In this paper, we present some upper bounds on bondage number for oriented graphs including tournaments, and symmetric planar digraphs.