Abstract
A dominating set D of G is a subset of V(G), such that every vertex in $$V(G){\setminus } D$$ is adjacent to at least one vertex in D. A neighborhood total dominating set, abbreviated for NTD set D, is a dominating set of G with an extra property: the subgraph induced by the open neighborhood of D, denoted by G[N(D)], has no isolated vertices. The neighborhood total domination number, denoted by $$\gamma _{nt}(G)$$ , is the minimum cardinality of an NTD set in G. A classical result of Vizing relates the size and the domination number of a graph of given order. In this paper, we present a Vizing-like result for $$\gamma _{nt}(G)$$ . Some results for $$\gamma _{nt}(G)$$ in terms of other graphic parameters, such as girth, diameter, and degree of G, are also obtained.
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