Vertex reconstruction in Cayley graphs

Author Elena Konstantinova

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Elena Konstantinova

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Elena Konstantinova. Vertex reconstruction in Cayley graphs. In Combinatorial and Algorithmic Foundations of Pattern and Association Discovery. Dagstuhl Seminar Proceedings, Volume 6201, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


In this report paper we collect recent results on the vertex reconstruction in Cayley graphs $Cay(G,S)$. The problem is stated as the problem of reconstructing a vertex from the minimum number of its $r$-neighbors that are vertices at distance at most $r$ from the unknown vertex. The combinatorial properties of Cayley graphs on the symmetric group $Sn$ and the signed permutation group $Bn$ with respect to this problem are presented. The sets of generators of $S$ are specified by applications in coding theory, computer science, molecular biology and physics.
  • Reconstruction problems
  • Cayley graphs
  • the symmetric group
  • the signed permutation group
  • sorting by reversals
  • pancake problem


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