Geodesic
CN-edge domination in graphs
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 11-17

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G=(V,E)$ be a graph. A subset $D$ of $V$ is called common neighbourhood dominating set (CN-dominating set) if for every $v\in V-D$ there exists a vertex $u\in D$ such that $uv\in E(G)$ and $|\Gamma(u,v)|\geq1$, where $|\Gamma(u,v)|$ is the number of common neighbourhood between the vertices $u$ and $v$. The minimum cardinality of such CN-dominating set denoted by $\gamma_{cn}(G)$ and is called common neighbourhood domination number (CN-edge domination) of $G$. In this paper we introduce the concept of common neighbourhood edge domination (CN-edge domination) and common neighbourhood edge domatic number (CN-edge domatic number) in a graph, exact values for some standard graphs, bounds and some interesting results are established. 
@article{VMJ_2013_15_2_a1,
     author = {A. Alwardi and N. D. Soner},
     title = {CN-edge domination in graphs},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {11--17},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a1/}
}
TY  - JOUR
AU  - A. Alwardi
AU  - N. D. Soner
TI  - CN-edge domination in graphs
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 11
EP  - 17
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a1/
LA  - en
ID  - VMJ_2013_15_2_a1
ER  - 
%0 Journal Article
%A A. Alwardi
%A N. D. Soner
%T CN-edge domination in graphs
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 11-17
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a1/
%G en
%F VMJ_2013_15_2_a1
A. Alwardi; N. D. Soner. CN-edge domination in graphs. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 2, pp. 11-17. http://geodesic.mathdoc.fr/item/VMJ_2013_15_2_a1/