For a graph G a subset D of the vertex set of G is a k-dominating set if every vertex not in D has at least k neighbors in D. The
k-domination number γk(G) is the minimum cardinality among the k-dominating sets of G. Note that the 1-domination number $γ_1(G)$ is the usual domination number γ(G).
Fink and Jacobson showed in 1985 that the inequality γk(G) ≥ γ(G)+k−2 is valid for every connected graph G. In this paper,
we recompile results concerning the case k = 2, where γk can be equal to γ. In particular, we present the characterization of different graph classes with equal domination and 2-domination numbers as are the cactus graphs, the claw-free graphs and the line graphs.
CitationHansberg, Adriana. Graphs with equal domination and 2-domination numbers. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 285-293.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: email@example.com