Bounds on neighborhood total domination in graphs
نویسندگان
چکیده
In this paper, we continue the study of neighborhood total domination in graphs first studied by Arumugam and Sivagnanam [S. Arumugam, C. Sivagnanam, Neighborhood total domination in graphs, Opuscula Math. 31 (2011) 519–531]. A neighborhood total dominating set, abbreviated NTD-set, in a graph G is a dominating set S in G with the property that the subgraph induced by the open neighborhood of the set S has no isolated vertex. The neighborhood total domination number, denoted by γnt(G), is the minimum cardinality of a NTD-set of G. Every total dominating set is a NTD-set, implying that γ (G) ≤ γnt(G) ≤ γt(G), whereγ (G) andγt(G)denote the domination and total domination numbers of G, respectively. We show that if G is a connected graph on n ≥ 3 vertices, then γnt(G) ≤ (n + 1)/2 and we characterize the graphs achieving equality in this bound. © 2013 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Applied Mathematics
دوره 161 شماره
صفحات -
تاریخ انتشار 2013