TY - MGZN
AU - Hernando, M.
AU - Mora, M.
AU - Pelayo, I. M.
T2 - ARS Mathematica Contemporanea
Y1 - 2015
VL - 8
IS - 2
SP - 365
EP - 379
UR - http://amc-journal.eu/index.php/amc/article/view/591/799
AB - 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.
TI - On global location-domination in graphs
ER -