Geodesic
Minimal edge extensions of some precomplete graphs
Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 105-117

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We consider the minimal edge $k$-extensions of precomplete graphs – graphs in which there is a vertex adjacent to all other vertices. The lemma about the marginal value of $k$ when a precomplete graph can have a minimal edge $k$-extension is proved. The full description of all the minimal edge $k$-extensions of precomplete graphs being joins of a complete graph and an empty graph, a chain or a cycle is given.
Keywords: precomplete graph, minimal edge extension, fault tolerance. 
@article{PDM_2010_1_a7,
     author = {M. B. Abrosimov},
     title = {Minimal edge extensions of some precomplete graphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {105--117},
     publisher = {mathdoc},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_1_a7/}
}
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M. B. Abrosimov. Minimal edge extensions of some precomplete graphs. Prikladnaâ diskretnaâ matematika, no. 1 (2010), pp. 105-117. http://geodesic.mathdoc.fr/item/PDM_2010_1_a7/