Geodesic
About the lower bounds for the number of additional arcs in a minimal vertex 1-extension of oriented path
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 71-72

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A graph $G^*$ with $n + k$ vertices is vertex $k$-extension of a graph $G$ if every graph obtained by removing any $k$ vertices from $G^*$ contains $G$; it is called minimal vertex $k$-extension of $G$ if it has the least number of arcs among all vertex $k$-extensions of graph $G$ with $n+k$ vertices. A lower bound for the number of additional arcs in minimal vertex 1-extension of an oriented path is given.
Keywords: graph, minimal vertex extension, fault tolerance. 
@article{PDMA_2013_6_a31,
     author = {M. B. Abrosimov and O. V. Modenova},
     title = {About the lower bounds for the number of additional arcs in a minimal vertex 1-extension of oriented path},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {71--72},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a31/}
}
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M. B. Abrosimov; O. V. Modenova. About the lower bounds for the number of additional arcs in a minimal vertex 1-extension of oriented path. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 71-72. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a31/