Bounding the Locating-Total Domination Number of a Tree in Terms of Its Annihilation Number

oleh: Ning Wenjie, Lu Mei, Wang Kun

Format: Article
Diterbitkan: University of Zielona Góra 2019-02-01

Deskripsi

Suppose G = (V,E) is a graph with no isolated vertex. A subset S of V is called a locating-total dominating set of G if every vertex in V is adjacent to a vertex in S, and for every pair of distinct vertices u and v in V −S, we have N(u) ∩ S ≠ N(v) ∩ S. The locating-total domination number of G, denoted by γLt(G), is the minimum cardinality of a locating-total dominating set of G. The annihilation number of G, denoted by a(G), is the largest integer k such that the sum of the first k terms of the nondecreasing degree sequence of G is at most the number of edges in G. In this paper, we show that for any tree of order n ≥ 2, γLt(T) ≤ a(T) + 1 and we characterize the trees achieving this bound.