Geodesic
Hereditary Equality of Domination and Exponential Domination
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 275-285.

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We characterize a large subclass of the class of those graphs G for which the exponential domination number of H equals the domination number of H for every induced subgraph H of G.
Keywords: domination, exponential domination, hereditary class 
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Henning, Michael A.; Jäger, Simon; Rautenbach, Dieter. Hereditary Equality of Domination and Exponential Domination. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 275-285. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a21/

[1] M. Anderson, R.C. Brigham, J.R. Carrington, R.P. Vitray and J. Yellen, On exponential domination of Cm × Cn, AKCE Int. J. Graphs Comb. 6 (2009) 341–351.

[2] A. Aytaç and B. Atay, On exponential domination of some graphs, Nonlinear Dyn. Syst. Theory 16 (2016) 12–19.

[3] S. Bessy, P. Ochem and D. Rautenbach, Bounds on the exponential domination number, Discrete Math. 340 (2017) 494–503. doi:10.1016/j.disc.2016.08.024

[4] S. Bessy, P. Ochem and D. Rautenbach, Exponential domination in subcubic graphs, Electron. J. Comb. 23 (2016) #P4.42.

[5] P. Dankelmann, D. Day, D. Erwin, S. Mukwembi and H. Swart, Domination with exponential decay, Discrete Math. 309 (2009) 5877–5883. doi:10.1016/j.disc.2008.06.040

[6] T.W. Haynes, S.T Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).

[7] M.A. Henning, Distance domination in graphs, in: T.W. Haynes, S.T. Hedetniemi and P.J. Slater (Eds.), Domination in Graphs: Advanced Topics, Marcel Dekker, New York (1998) 321–349.

[8] M.A. Henning, S. Jäger and D. Rautenbach, Relating domination, exponential domination, and porous exponential domination, Discrete Optim. 23 (2017) 81–92. doi:0.1016/j.disopt.2016.12.002

[9] E.S. Wolk, A note on “the comparability graph of a tree”, Proc. Amer. Math. Soc. 16 (1965) 17–20.