Mixed Roman Domination in Graphs

Adabi, M., Ebrahimi Targhi, E., Jafari Rad, N., Moradi, M.S.: Properties of independent Roman domination in graphs. Australas. J. Combin. 52, 11–18 (2012)

Alavi, Y., Behzad, M., Lesniak, L., Nordhaus, E.A.: Total matchings and total coverings of graphs. J. Graph Theory 1, 135–140 (1977)

Alavi, Y., Liu, J.Q., Wang, J.F., Zhang, Z.F.: On total covers of graphs. Discret. Math. 100(13), 229–233 (1992)

Bermudo, S., Fernau, H., Sigarreta, J.M.: The differential and the Roman domination number of a graph. Appl. Anal. Discret. Math. 8, 155–171 (2014)

Chellali, M., Jafari Rad, N.: A note on the independent Roman domination in unicyclic graphs. Opusc. Math. 32, 715–718 (2012)

Chellali, M., Jafari Rad, N.: Strong equality between the Roman domination and independent Roman domination numbers in trees. Discuss. Math. Graph Theory 33, 337–346 (2013)

Cockayne, E.J., Goodman, S., Hedetniemi, S.: A linear algorithm for the domination number of a tree. Inf. Process. Lett. 4, 41–44 (1975)

Cockayne, E.J., Dreyer Sr, P.M., Hedetniemi, S.M., Hedetniemi, S.T.: On Roman domination in graphs. Discret. Math. 278, 11–22 (2004)

Ebrahimi Targhi, E., Jafari Rad, N., Mynhardt, C.M., Wu, Y.: Bounds for the independent Roman domination number in graphs. J. Combin. Math. Combin. Comput. 80, 351–365 (2012)

Erdös, P., Meir, A.: On total matching numbers and total covering numbers of complementary graphs. Discret. Math. 19, 229–233 (1977)

Hatami, P.: An approximation algorithm for the total covering problem. Discuss. Math. Graph Theory 27(3), 553–558 (2007)

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

Hedetniemi, S.T., Rubalcaba, R.R., Slater, P.J., Walsh, M.: Few compare to the great Roman empire. Congr. Numer. 217, 129–136 (2013)

Lan, J.K., Chang, G.J.: On the mixed domination problem in graphs. Theor. Comput. Sci. 476, 84–93 (2013)

ReVelle, C.S., Rosing, K.E.: Defendens imperium romanum: a classical problem in military strategy. Am. Math. Monthly 107(7), 585–594 (2000)

Stewart, I.: Defend the Roman Empire!. Sci. Am. 281(6), 136–139 (1999)

West, D.B.: Introduction to Graph Theory, 2nd edn. Prentice Hall, Upper Saddle River (2001)

Zhao, Y., Kang, L., Sohn, M.Y.: The algorithmic complexity of mixed domination in graphs. Theor. Comput. Sci. 412, 2387–2392 (2011)