164 research outputs found
Half domination arrangements in regular and semi-regular tessellation type graphs
We study the problem of half-domination sets of vertices in vertex transitive
infinite graphs generated by regular or semi-regular tessellations of the
plane. In some cases, the results obtained are sharp and in the rest, we show
upper bounds for the average densities of vertices in half-domination sets.Comment: 14 pages, 12 figure
Eternal dominating sets on digraphs and orientations of graphs
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.Comment: 34 page
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