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Abstract
A vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove that for every nontrivial tree T of order n, with l leaves and s support vertices we have γ_d^{oi}(T) ≤ (2n+l+s)/3, and we characterize the trees attaining this upper bound.
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1515/gmj-2014-0057
- License
- Copyright (2015 De Gruyter)
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Georgian Mathematical Journal
no. 22,
edition 1,
pages 105 - 109,
ISSN: 1072-947X - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Krzywkowski M.: An upper bound for the double outer-independent domination number of a tree// Georgian Mathematical Journal. -Vol. 22, iss. 1 (2015), s.105-109
- DOI:
- Digital Object Identifier (open in new tab) 10.1515/gmj-2014-0057
- Verified by:
- Gdańsk University of Technology
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