### Bounds for the $m$-Eternal Domination Number of a Graph

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A.P. Burger, E.J. Cockayne, W.R. Grundlingh, C.M. Mynhardt, J.H. van Vuuren, W. Winterbach, Infinite order domination in graphs. J.Combin. Math. Combin. Comput. 50 (2004), 179--194.

E. Chambers, W. Kinnersly, N. Prince, Mobile eternal security in graphs, manuscript (2008).

S. Finbow, M.-E. Messinger, M. van Bommel, Eternal domination in $3 times n$ grids. Australas. J. Combin. 61 (2015), 156-174.

W. Goddard, S.M. Hedetniemi, S.T. Hedetniemi, Eternal security in graphs, J. Combin. Math. Combin. Comput. 52 (2005), 169-180.

J. Goldwasser, W. Klostermeyer, C. M. Mynhardt, Eternal protection in grid graphs. Utilitas Math. ~textbf{91} (2013), 47--64.

T. W. Haynes, S. T. Hedetniemi, P. J. Slater, Fundamentals of Domination in Graphs. Marcel Dekker, New York, 1998.

M. A. Henning, I. Schiermeyer, A. Yeo, A new bound on the domination number of graphs with minimum degree two, Electronic Journal of Combinatorics 18 (2011), paper P12.

W. Klostermeyer, G. MacGillivray, Eternally secure sets, independence sets, and Cliques. AKCE Int. J. Graphs Comb. 2 (2005), 119-122.

W. Klostermeyer, G. MacGillivray, Eternal dominating sets in graphs, J. Combin. Math. Combin. Comput. 68 (2009), 97-111.

W. Klostermeyer, G. MacGillivray, Eternal domination in trees, to appear in J. Combin. Math. Combin. Comput. (2015).

W. Klostermeyer, C.M.~Mynhardt, Vertex covers and eternal dominating sets, Discrete Applied Mathematics 160 (2012), pp. 1183-1190.

W. Klostermeyer, C.~M.~Mynhardt, Protecting a graph with mobile guards, http://arxiv.org/abs/1407.5228

A. Kostochka, B. Stodolsky, On domination in connected cubic graphs, Discrete Math. 304 (2005), pp. 45--50.

A. V. Kostochka, C. Stocker, A new bound on the domination number of connected cubic graphs. Sib. Elektron. Mat. Izv. 6 (2009), 465–504.

W. McCuaig, B. Shepherd, Domination in graphs with minimum degree two. J. Graph Theory 13 (1989), 749-762.

O. Ore, Theory of graphs. Amer. Math. Soc. Transl. 38 (Amer. Math. Soc., Providence, RI, 1962), 206--212.

J. Petersen, Die theorie der regulären graphs, Acta Mathematica 15 (1891), pp. 193-220.

B. Reed, Paths, stars, and the number three, Combin. Probab. Comput. 5 (1996), pp. 277--295.

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by haytham هاوس (2018-05-05)