Geodesic
A note on automorphisms of the infinite-dimensional hypercube graph
Mark Pankov1
1Department of Mathematics and Computer Science, University of Warmia and Mazury
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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We define the infinite-dimensional hypercube graph $H_{{\aleph}_{0}}$ as a graph whose vertex set is formed by the so-called singular subsets of ${\mathbb Z}\setminus\{0\}$. This graph is not connected, but it has isomorphic connected components. We show that the restrictions of its automorphisms to the connected components are induced by permutations on ${\mathbb Z}\setminus\{0\}$ preserving the family of singular subsets. As an application, we describe the automorphism group of the connected components.
DOI : 10.37236/2749
Classification : 05C63, 05C65, 05C60, 20B27
Mots-clés : infinite-dimensional hypercube graph, graph automorphism, weak wreath product of groups

Mark Pankov  1

1 Department of Mathematics and Computer Science, University of Warmia and Mazury 
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Mark Pankov. A note on automorphisms of the infinite-dimensional hypercube graph. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2749

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