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Eternal dominating sets on digraphs and orientations of graphs

Authors :
Bagan, Guillaume
Joffard, Alice
Kheddouci, Hamamache
Publication Year :
2018

Abstract

We study the eternal dominating number and the m-eternal dominating number on digraphs. We generalize known results on graphs to digraphs. We also consider the problem "oriented (m-)eternal domination", consisting in finding an orientation of a graph that minimizes its eternal dominating number. We prove that computing the oriented eternal dominating number is NP-hard and characterize the graphs for which the oriented m-eternal dominating number is 2. We also study these two parameters on trees, cycles, complete graphs, complete bipartite graphs, trivially perfect graphs and different kinds of grids and products of graphs.<br />Comment: 34 pages

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1805.09623
Document Type :
Working Paper