Abstract
A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set in G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we investigate relationships between the annihilation number and the total domination number of a graph. Let T be a tree of order n<2. We show that γt(T)≤a(T)+1, and we characterize the extremal trees achieving equality in this bound.
Original language | English |
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Pages (from-to) | 349-354 |
Number of pages | 6 |
Journal | Discrete Applied Mathematics |
Volume | 161 |
Issue number | 3 |
DOIs | |
Publication status | Published - Feb 2013 |
Keywords
- Annihilation number
- Total domination
- Total domination number
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics