Connected domination critical graphs with cut vertices
Nawarat Ananchuen, Pawaton Kaemawichanurat · Discussiones Mathematicae Graph Theory · 2018
A graph G is said to be k- c -critical if the connected domination number of G, c (G), is k and c (G + uv) < k for any pair of non-adjacent vertices u and v of G. Let G be a k- c -critical graph and (G) the number of cut vertices of G. It was proved, in In this paper, we generalize that every k- ccritical graph satisfies (G) k -2 for all k 5. We also characterize all k- c -critical graphs when (G) is achieving the upper bound.