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2015•Unpublished venueRequires access

ON TREES ATTAINING AN UPPER BOUND ON THE TOTAL DOMINATION NUMBER

Marcin Krzywkowski

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Abstract

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 γt(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, γt(T) ≤ (n+ s)/2. We characterize all trees attaining this upper bound. 1.

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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 γt(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, γt(T) ≤ (n+ s)/2. We characterize all trees attaining this upper bound. 1.

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Available abstract

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 γt(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, γt(T) ≤ (n+ s)/2. We characterize all trees attaining this upper bound. 1.

Key concepts: Domination analysis, Mathematics, Combinatorics, Dominating set, Upper and lower bounds, Vertex (graph theory), Graph, Cardinality (data modeling)

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