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Abstract
A total outer-independent dominating set of a graph 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 nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3, and we characterize the trees attaining this lower bound.
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- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.crma.2010.11.021
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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COMPTES RENDUS MATHEMATIQUE
no. 349,
pages 7 - 9,
ISSN: 1631-073X - Language:
- English
- Publication year:
- 2011
- Bibliographic description:
- Krzywkowski M.: A lower bound on the total outer-independent domination number of a tree// COMPTES RENDUS MATHEMATIQUE. -Vol. 349, nr. Iss. 1 (2011), s.7-9
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.crma.2010.11.021
- Verified by:
- Gdańsk University of Technology
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