Geodesic
Automorphisms of kaleidoscopical graphs
Algebra and discrete mathematics, no. 2 (2007), pp. 125-129 Cet article a éte moissonné depuis la source Math-Net.Ru

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A regular connected graph $\Gamma$ of degree $s$ is called kaleidoscopical if there is a $(s+1)$-coloring of the set of its vertices such that every unit ball in $\Gamma$ has no distinct monochrome points. The kaleidoscopical graphs can be considered as a graph counterpart of the Hamming codes. We describe the groups of automorphisms of kaleidoscopical trees and Hamming graphs. We show also that every finitely generated group can be realized as the group of automorphisms of some kaleidoscopical graphs.
Keywords: kaleidoscopical graph, Hamming pair, kaleidoscopical tree. 
@article{ADM_2007_2_a11,
     author = {I. V. Protasov and K. D. Protasova},
     title = {Automorphisms of kaleidoscopical graphs},
     journal = {Algebra and discrete mathematics},
     pages = {125--129},
     year = {2007},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_2_a11/}
}
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I. V. Protasov; K. D. Protasova. Automorphisms of kaleidoscopical graphs. Algebra and discrete mathematics, no. 2 (2007), pp. 125-129. http://geodesic.mathdoc.fr/item/ADM_2007_2_a11/