Vertex reconstruction in Cayley graphs

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 S of generators are specified by applications in coding theory, computer science, molecular biology and physics. Key words: reconstruction problems; Cayley graphs; symmetric group; signed permutation group; sorting by reversals; pancake problem;

• Type: Conference
• Year: 2006
• Where: DAGSTUHL
• Authors: Elena V. Konstantinova
• Keywords: Cayley Graphs, DAGSTUHL 2006, DAGSTUHL 2007, Signed Permutation Group, Symmetric Group