V. I. Trofimov, “The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 3,Pages <nobr>303

This article is cited in 1 paper

The finiteness of the number of symmetrical extensions of a locally finite tree by a finite graph

V. I. Trofimov^ab

^a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
^b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: We prove that there are only finitely many symmetrical extensions of a locally finite tree by a finite graph. Moreover, we prove that there are only finitely many pairwise nonequivalent realizations of symmetrical extensions of a locally finite tree by a finite graph.

Keywords: tree, symmetrical extension by a finite graph.

UDC: 512.54+519.17

Received: 01.06.2015