Geodesic
Minimal vertex $1$-extensions of palm trees
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 233-241.

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Minimal vertex $1$-extension of graphs can be regarded as a model of optimal $1$-node fault tolerant implementation of a system. This paper is about of the $1$-vertex extensions of a graphs from a special class named palm trees.This article presents a solution to the problem of finding the minimal vertex $1$-extension of palm trees with two leafs. 
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D. D. Komarov. Minimal vertex $1$-extensions of palm trees. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 2, pp. 233-241. http://geodesic.mathdoc.fr/item/ISU_2014_14_2_a11/

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