Geodesic
Graphs with equal domination and 2-distance domination numbers
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 375-385 Cet article a éte moissonné depuis la source Library of Science

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Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum cardinality of a 2-distance dominating set of G. We characterize all trees and all unicyclic graphs with equal domination and 2-distance domination numbers.
Keywords: domination number, trees, unicyclic graphs 
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Raczek, Joanna. Graphs with equal domination and 2-distance domination numbers. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 2, pp. 375-385. http://geodesic.mathdoc.fr/item/DMGT_2011_31_2_a12/

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