Roman bondage in graphs
Nader Jafari Rad ; Lutz Volkmann
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 763-773 / Harvested from The Polish Digital Mathematics Library
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A Roman dominating function on a graph G is a function f:V(G) → 0,1,2 satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V(G))=∑u∈V(G)f(u). The Roman domination number, γR(G), of G is the minimum weight of a Roman dominating function on G. In this paper, we define the Roman bondage bR(G) of a graph G with maximum degree at least two to be the minimum cardinality of all sets E’ ⊆ E(G) for which γR(G-E')>γR(G). We determine the Roman bondage number in several classes of graphs and give some sharp bounds.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:270940 
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Nader Jafari Rad; Lutz Volkmann. Roman bondage in graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 763-773. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1578/

[000] [1] D. Bauer, F. Harary, J. Nieminen and C.L. Suffel, Domination alteration sets in graphs, Discrete Math. 47 (1983) 153-161, doi: 10.1016/0012-365X(83)90085-7. | Zbl 0524.05040

[001] [2] E.J. Cockayne, P.M. Dreyer Jr., S.M. Hedetniemi and S.T. Hedetniemi, Roman domination in graphs, Discrete Math. 278 (2004) 11-22, doi: 10.1016/j.disc.2003.06.004. | Zbl 1036.05034

[002] [3] J.E. Dunbar, T.W. Haynes, U. Teschner and L. Volkmann, Bondage, insensitivity, and reinforcement, in: T.W. Haynes, S.T. Hedetniemi, P.J. Slater (Eds.), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998) 471-489. | Zbl 0894.05025

[003] [4] J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, The bondage number of a graph, Discrete Math. 86 (1990) 47-57, doi: 10.1016/0012-365X(90)90348-L. | Zbl 0745.05056

[004] [5] B.L. Hartnell and D.F. Rall, Bounds on the bondage number of a graph, Discrete Math. 128 (1994) 173-177, doi: 10.1016/0012-365X(94)90111-2. | Zbl 0796.05051

[005] [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). | Zbl 0890.05002

[006] [7] C.S. ReVelle and K.E. Rosing, Defendens imperium romanum: a classical problem in military strategy, Amer Math. Monthly 107 (2000) 585-594, doi: 10.2307/2589113. | Zbl 1039.90038

[007] [8] I. Stewart, Defend the Roman Empire!, Sci. Amer. 281 (1999) 136-139, doi: 10.1038/scientificamerican1299-136.

[008] [9] U. Teschner, New results about the bondage number of a graph, Discrete Math. 171 (1997) 249-259, doi: 10.1016/S0012-365X(96)00007-6. | Zbl 0881.05067

[009] [10] D.B. West, Introduction to Graph Theory, (2nd edition) (Prentice Hall, USA, 2001).