Geodesic
On a counterexample to a minimal vertex $1$-extension of starlike trees
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 83-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a given graph $G$ with $n$ nodes, we say that graph $G^*$ is its vertex extension if for each vertex $v$ of $G^*$ the subgraph $G^*-v$ contains graph $G$ up to isomorphism. A graph $G^*$ is a minimal vertex extension of the graph $G$ if $G^*$ has $n+1$ nodes and there is no vertex extension with $n+1$ nodes of $G$ having fewer edges than $G^*$. A tree is called starlike if it has exactly one node of degree greater than two. We give a lower and upper bounds of the edge number of a minimal vertex extension of a starlike tree and present trees for which these bounds are achieved. 
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     title = {On a~counterexample to a~minimal vertex $1$-extension of starlike trees},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {83--84},
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}
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M. B. Abrosimov; D. D. Komarov. On a counterexample to a minimal vertex $1$-extension of starlike trees. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 83-84. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a41/

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[3] Abrosimov M. B., Komarov D. D., Minimalnye vershinnye rasshireniya sverkhstroinykh derevev s malym chislom vershin, Dep. v VINITI 18.10.2010, No 7590-V, SGU, Saratov, 2010, 38 pp.