On locating-domination in graphs

Mustapha Chellali; Malika Mimouni; Peter J. Slater

Mustapha Chellali ; Malika Mimouni ; Peter J. Slater

Discussiones Mathematicae Graph Theory, Tome 30 (2010), p. 223-235 / Harvested from The Polish Digital Mathematics Library

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Résumé

A set D of vertices in a graph G = (V,E) is a locating-dominating set (LDS) if for every two vertices u,v of V-D the sets N(u)∩ D and N(v)∩ D are non-empty and different. The locating-domination number $γ_{L} (G)$ is the minimum cardinality of a LDS of G, and the upper locating-domination number, $Γ_{L} (G)$ is the maximum cardinality of a minimal LDS of G. We present different bounds on $Γ_{L} (G)$ and $γ_{L} (G)$ .

Publié le : 2010-01-01

Zbl 1214.05104

EUDML-ID : urn:eudml:doc:270845

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Mustapha Chellali; Malika Mimouni; Peter J. Slater. On locating-domination in graphs. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 223-235. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1488/

Bibliographie

[000] [1] M. Blidia, M. Chellali and O. Favaron, Independence and 2-domination in trees, Australasian J. Combin. 33 (2005) 317-327. | Zbl 1081.05081

[001] [2] M. Blidia, M. Chellali, O. Favaron and N. Meddah, On k-independence in graphs with emphasis on trees, Discrete Math. 307 (2007) 2209-2216, doi: 10.1016/j.disc.2006.11.007. | Zbl 1123.05066

[002] [3] M. Blidia, M. Chellali, R. Lounes and F. Maffray, Characterizations of trees with unique minimum locating-dominating sets, submitted. | Zbl 1244.05164

[003] [4] M. Blidia, M. Chellali, F. Maffray, J. Moncel and A. Semri, Locating-domination and identifying codes in trees, Australasian J. Combin. 39 (2007) 219-232. | Zbl 1136.05049

[004] [5] M. Blidia, O. Favaron and R. Lounes, Locating-domination, 2-domination and independence in trees, Australasian J. Combin. 42 (2008) 309-316. | Zbl 1153.05039

[005] [6] M. Farber, Domination, independent domination and duality in strongly chordal graphs, Discrete Appl. Math. 7 (1984) 115-130, doi: 10.1016/0166-218X(84)90061-1. | Zbl 0531.05045

[006] [7] J.F. Fink, M.S. Jacobson, L.F. Kinch and J. Roberts, On graphs having domination number half their order, Period. Math. Hungar. 16 (1985) 287-293, doi: 10.1007/BF01848079. | Zbl 0602.05043

[007] [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). | Zbl 0890.05002

[008] [9] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). | Zbl 0883.00011

[009] [10] C. Payan and N.H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982) 23-32, doi: 10.1002/jgt.3190060104. | Zbl 0489.05049

[010] [11] G. Ravindra, Well covered graphs, J. Combin. Inform. System. Sci. 2 (1977) 20-21. | Zbl 0396.05007

[011] [12] P.J. Slater, Domination and location in acyclic graphs, Networks 17 (1987) 55-64, doi: 10.1002/net.3230170105. | Zbl 0643.90089

[012] [13] P.J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci. 22 (1988) 445-455. | Zbl 0656.05057