Geodesic
DEGREES, NEIGHBOURHOODS, AND CLOSURE OPERATIONS
Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1 
L. Stacho. DEGREES, NEIGHBOURHOODS, AND CLOSURE OPERATIONS. Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a5/
@article{AMUC_2000_69_1_a5,
     author = {L. Stacho},
     title = {DEGREES, {NEIGHBOURHOODS,} {AND} {CLOSURE} {OPERATIONS}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2000},
     volume = {69},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a5/}
}
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JO  - Acta mathematica Universitatis Comenianae
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%J Acta mathematica Universitatis Comenianae
%D 2000
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Voir la notice de l'article provenant de la source Comenius University

Closure theorems in graph theory are of the following type: Let $G$ be a graph, $\cal P$ a graph theoretic property, and let $u$ and $v$ be two non-adjacent vertices of $G$. If condition $c(u,v)$ holds, then $G$ has property $\cal P$ if and only if $G+uv$ has $\cal P$. We discuss several such results of the above type where the condition $c(u,v)$ refers to neighbourhood properties of $u$ and $v$.