Geodesic
The total vertex separation number of a graph
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 86-91 
P. A. Golovach. The total vertex separation number of a graph. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 86-91. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a7/
@article{DM_1997_9_4_a7,
     author = {P. A. Golovach},
     title = {The total vertex separation number of a graph},
     journal = {Diskretnaya Matematika},
     pages = {86--91},
     year = {1997},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a graph $G$ we introduce a new graph invariant $\operatorname{sv}(G)$ which we name the total vertex separation number. We demonstrate that the recognition problem consisting in checking whether or not $\operatorname{sv}(G)\le k$ for a given $G$ and a non-negative integer $k$ is NP-complete even for edge graphs. We consider the problem to calculate this invariant for the interval graphs. In addition, the total vertex separation number of a tree is considered. This research was supported by the program ‘Universities of Russia’.