On the Complexity of the Perfect Edge Domination Problem

Abstract

A perfect edge dominating set of G=(V,E) is a subset D of E such that every edge not in D is dominated by exactly one edge in D. The perfect edge domination problem is to find a perfect edge dominating set with the minimum cardinality in G. In this paper, we show that the perfect edge domination problem is NP-complete on bipartite graphs. Moreover, we present linear-time algorithms for solving the perfect edge domination problem on trees and series-parallel graphs.