2014
DOI: 10.1016/j.ejc.2013.04.009
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Nordhaus–Gaddum bounds for locating domination

Abstract: A dominating set S of graph G is called metric-locating-dominating if it is also locating, that is, if every vertex v is uniquely determined by its vector of distances to the vertices in S . If moreover, every vertex v not in S is also uniquely determined by the set of neighbors of v belonging to S , then it is said to be locating-dominating. Locating, metric-locating-dominating and locatingdominating sets of minimum cardinality are called β-codes, η-codes and λ-codes, respectively. A Nordhaus-Gaddum bound is … Show more

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Cited by 26 publications
(24 citation statements)
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References 11 publications
(17 reference statements)
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“…By Theorem 4.3, kðGÞ 6 n À CðGÞ for every twin-free graph G. Further, Theorem 7 of [25] gives jkðGÞ À kðGÞj 6 1 and so kðGÞ 6 kðGÞ þ 1 6 n À CðGÞ þ 1 since G is also twin-free. Therefore, kðGÞ 6 minfn À CðGÞ; n À CðGÞ þ 1g.…”
Section: ä åmentioning
confidence: 95%
“…By Theorem 4.3, kðGÞ 6 n À CðGÞ for every twin-free graph G. Further, Theorem 7 of [25] gives jkðGÞ À kðGÞj 6 1 and so kðGÞ 6 kðGÞ þ 1 6 n À CðGÞ þ 1 since G is also twin-free. Therefore, kðGÞ 6 minfn À CðGÞ; n À CðGÞ þ 1g.…”
Section: ä åmentioning
confidence: 95%
“…Proof. The values of the location-domination number of all these families, except the wheels, are already known (see [1,12,18]). Next, let us calculate the values of the location-domination number for the wheels and for the complements of all these families and also, from the results previously proved, the global location-domination number of them.…”
Section: The Global Location-domination Numbermentioning
confidence: 99%
“…Notice also that a locating-dominating set is both a locating set and a dominating set, and thus β(G) ≤ λ(G) and γ(G) ≤ λ(G). LDcodes and the location-domination parameter have been intensively studied during the last decade; see [1,2,5,8,12] A complete and regularly updated list of papers on locating dominating codes is to be found in [14].…”
mentioning
confidence: 99%
“…Certainly, every LD-set of a non-connected graph G is the union of LD-sets of its connected components and the location-domination number is the sum of the location-domination number of its connected components. Both, LD-codes and the location-domination parameter have been intensively studied during the last decade; see [1,2,3,5,6,8,9,10]. A complete and regularly updated list of papers on locating-dominating codes is to be found in [11].…”
Section: Introductionmentioning
confidence: 99%