Geodesic
Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension
Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 111-120

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

A graph $G^*$ is $k$-vertex extension of graph $G$ if every graph obtained by removing any $k$ vertices from $G^*$ contains $G$. $k$-Vertex extension of graph $G$ with $n+k$ vertices is called minimal if, among all $k$-vertex extensions of graph $G$ with $n+k$ vertices, it has the minimum possible number of edges. The graphs whose minimal vertex 1-extensions have a specified number of additional edges are studied. A solution is given when the number of additional edges is equal to one, two or three.
Keywords: graph, minimal vertex extension, exact vertex extension, fault tolerance. 
@article{PDM_2012_1_a7,
     author = {M. B. Abrosimov},
     title = {Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {111--120},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_1_a7/}
}
TY  - JOUR
AU  - M. B. Abrosimov
TI  - Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2012
SP  - 111
EP  - 120
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2012_1_a7/
LA  - ru
ID  - PDM_2012_1_a7
ER  - 
%0 Journal Article
%A M. B. Abrosimov
%T Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension
%J Prikladnaâ diskretnaâ matematika
%D 2012
%P 111-120
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2012_1_a7/
%G ru
%F PDM_2012_1_a7
M. B. Abrosimov. Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension. Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 111-120. http://geodesic.mathdoc.fr/item/PDM_2012_1_a7/