Relating the annihilation number and the total domination number of a tree

Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

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 languageEnglish
Pages (from-to)349-354
Number of pages6
JournalDiscrete Applied Mathematics
Volume161
Issue number3
DOIs
Publication statusPublished - Feb 2013

Keywords

  • Annihilation number
  • Total domination
  • Total domination number

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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