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Abstract
A total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have gamma_t^{oi}(T) >= (2n+s-l)/3, and we characterize the trees attaining this upper bound.
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- DOI:
- Digital Object Identifier (open in new tab) 10.7494/opmath.2012.32.1.153
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- Category:
- Articles
- Type:
- artykuły w czasopismach recenzowanych i innych wydawnictwach ciągłych
- Published in:
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Opuscula Mathematica
no. 32,
pages 153 - 158,
ISSN: 1232-9274 - Language:
- English
- Publication year:
- 2012
- Bibliographic description:
- Krzywkowski M.: An upper bound on the total outer-independent domination number of a tree// Opuscula Mathematica. -Vol. 32., iss. Iss. 1 (2012), s.153-158
- DOI:
- Digital Object Identifier (open in new tab) 10.7494/opmath.2012.32.1.153
- Verified by:
- Gdańsk University of Technology
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