Geodesic
On global location-domination in graphs
Ars Mathematica Contemporanea, Tome 8 (2015) no. 2, pp. 365-379.

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A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number lambda(G). An LD-set S of a graph G is  global if it is an LD-set of both G and its complement G'. The global location-domination number lambda g(G) is introduced as  the minimum cardinality of a global LD-set of G.In this paper, some general relations between  LD-codes and the location-domination number in a graph and its complement are presented first. Next, a number of basic properties involving the global location-domination number are showed. Finally, both parameters are studied in-depth for the family of block-cactus graphs.
DOI : 10.26493/1855-3974.591.5d0
Keywords: Domination, global domination, locating domination, complement graph, block-cactus. 
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Carmen Hernando; Merce Mora; Ignacio M. Pelayo. On global location-domination in graphs. Ars Mathematica Contemporanea, Tome 8 (2015) no. 2, pp. 365-379. doi : 10.26493/1855-3974.591.5d0. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.591.5d0/

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