On global location-domination in graphs

Carmen Hernando, Merce Mora, Ignacio M. Pelayo

Abstract


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.


Keywords


Domination, global domination, locating domination, complement graph, block-cactus.

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DOI: https://doi.org/10.26493/1855-3974.591.5d0

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications