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Diskretnyi Analiz i Issledovanie Operatsii, Ser. 1, 2001, Volume 8, Issue 3, Pages 73–80
(Mi da226)
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On the isometric embedding of arbitrary graphs into a graph of a given diameter possessing the metric continuation property
V. A. Tashkinov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We prove that an arbitrary ordinary graph $G$ can be embedded as a generated subgraph into a graph $H$ of given diameter $d(H)=d\geqslant 2$ in which any two vertices lie on some diametral path. If the diameter $d(G)$ of $G$ is less than or equal to $d$, then the embedding can be achieved isometrically, that is, with preservation of the distances between the vertices in $G$.
Received: 29.06.2001
Citation:
V. A. Tashkinov, “On the isometric embedding of arbitrary graphs into a graph of a given diameter possessing the metric continuation property”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:3 (2001), 73–80
Linking options:
https://www.mathnet.ru/eng/da226 https://www.mathnet.ru/eng/da/v8/s1/i3/p73
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Abstract page: | 369 | Full-text PDF : | 79 |
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