Geodesic
Connected Domination Critical Graphs with Cut Vertices
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1035-1055.

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A graph G is said to be k-γc-critical if the connected domination number of G, γc(G), is k and γc(G + uv) lt; k for any pair of non-adjacent vertices u and v of G. Let G be a k-γc-critical graph and ζ (G) the number of cut vertices of G. It was proved, in [1, 6], that, for 3 ≤ k ≤ 4, every k-γc-critical graph satisfies ζ (G) ≤ k − 2. In this paper, we generalize that every k-γc-critical graph satisfies ζ (G) ≤ k − 2 for all k ≥ 5. We also characterize all k-γc-critical graphs when ζ(G) is achieving the upper bound.
Keywords: connected domination, critical 
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Kaemawichanurat, Pawaton; Ananchuen, Nawarat. Connected Domination Critical Graphs with Cut Vertices. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 4, pp. 1035-1055. http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a6/

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