Mar 4, 2015 · Abstract A set S of vertices in graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum ...
These graphs we call γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We verify an open problem of k-γt-critical graphs .
The existence problem of the total domination vertex critical graphs has been studied in a series of articles. We first settle the existence problem with ...
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Jan 6, 2010 · Abstract. The existence problem of the total domination vertex critical graphs has been studied in a series of articles.
Mar 12, 2011 · Abstract. Let γt(G) be the total domination number of graph G, a graph G is k-total domination vertex critical (or just k-γt-critical) if ...
Theorem 13 For all k ≡ 2 (mod 3), there exists a k-γt-critical graph of diameter (5k −. 7)/3. Proof. For q ≥ 0, define the pointed graph Yq = F ◦ Q ...
A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total ...
On the existence of (k,l)-critical graphs ... Recommendations. The Existence Problem of k-yt-Critical Graphs ... On 4-γt -critical graphs of diameter two. A vertex ...
Mar 24, 2016 · Abstract. A graph G is said to be k-γt-critical if the total domination number γt(G) = k and γt(G + uv) < k for every uv /∈ E(G).
Mojdeh and Rad [6] proposed an open problem: Does there exist a 3-γt-critical graph G of order Δ(G) + 3 with Δ(G) odd? In this paper, we prove that there exists ...