✦ LIBER ✦

On semigroups of graph endomorphisms

✍ Scribed by S. Foldes; G. Sabidussi

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 358 KB
Volume: 30
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90113-2

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that given a finite or infinite graph H and a subsemigroup B of its endomorphism semigroup End H, there exists a graph G such that (i) H is an induced subgraph of G, (ii) H is stable by every fe End 6.

(iii) every f~ End G is uniquely determined by its restriction to H, (iv) the restriction of End G to H is precisel:, B.

On montre qu'etant donne un graphe tini ou infini H et un sous-demigroupe quelconque B dc son demigroupe d'endomorphismes End H, il cxiste un graphe G tel que (i) H est un sous-graphe plein de G, (ii) H est stable pour tout f~ End G, (iii) chaque f~ End G est determine d'une faGon unique par sa restriction a Z-Z, (iv) la restriction de End G a H est precisernent B.

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