Abstract
For a graph G = (V, E), a subset D ⊆ V(G) is a 2-dominating set if every vertex of V(G)\D has at least two neighbors in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees with equal 2-domination and 2-outer-independent domination numbers.
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Research supported by the Polish Ministry of Science and Higher Education grant IP/2012/038972.
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Krzywkowski, M. On trees with equal 2-domination and 2-outer-independent domination numbers. Indian J Pure Appl Math 46, 191–195 (2015). https://doi.org/10.1007/s13226-015-0126-7
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DOI: https://doi.org/10.1007/s13226-015-0126-7