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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2020_40_4_a6,
     author = {Kaemawichanurat, Pawaton and Ananchuen, Nawarat},
     title = {Connected {Domination} {Critical} {Graphs} with {Cut} {Vertices}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {1035--1055},
     publisher = {mathdoc},
     volume = {40},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a6/}
}
TY  - JOUR
AU  - Kaemawichanurat, Pawaton
AU  - Ananchuen, Nawarat
TI  - Connected Domination Critical Graphs with Cut Vertices
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2020
SP  - 1035
EP  - 1055
VL  - 40
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a6/
LA  - en
ID  - DMGT_2020_40_4_a6
ER  - 
%0 Journal Article
%A Kaemawichanurat, Pawaton
%A Ananchuen, Nawarat
%T Connected Domination Critical Graphs with Cut Vertices
%J Discussiones Mathematicae. Graph Theory
%D 2020
%P 1035-1055
%V 40
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2020_40_4_a6/
%G en
%F DMGT_2020_40_4_a6
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/