2-Outer-Independent Domination in Graphs

We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V ( G ) \ D has at least two neighbors in D , and the set V ( G ) \ D is independent. The 2-outer-independent domination number o...

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Bibliographic Details
Published in:National Academy science letters 2015-06, Vol.38 (3), p.263-269
Main Authors: Jafari Rad, Nader, Krzywkowski, Marcin
Format: Article
Language:English
Subjects:
History of Science
Humanities and Social Sciences
multidisciplinary
Research Article
Science
Science (multidisciplinary)
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Summary:We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V ( G ) \ D has at least two neighbors in D , and the set V ( G ) \ D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G . We show that if a graph has minimum degree at least two, then its 2-outer-independent domination number equals the vertex cover number. Then we investigate the 2-outer-independent domination in graphs with minimum degree one.
ISSN:0250-541X
2250-1754
DOI:10.1007/s40009-015-0389-x