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Abstract
A total 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. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination number of a tree in terms of the order and the number of support vertices, γ_t(T ) ≤ (n+s)/2. We characterize all trees attaining this upper bound.
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
-
Bulletin of the Iranian Mathematical Society
no. 41,
edition 6,
pages 1339 - 1344,
ISSN: 1017-060X - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Krzywkowski M.: On trees attaining an upper bound on the total domination number// Bulletin of the Iranian Mathematical Society. -Vol. 41, iss. 6 (2015), s.1339-1344
- Verified by:
- Gdańsk University of Technology
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