Contract grant sponsor: Australian Research Council; contract grant number: DP1093320; contract grant sponsor: Fonds National de la Recherche, Luxembourg, co-funded under the Marie Curie Actions of the European Commission; contract grant number: FP7-COFUND.
Switching Reconstruction of Digraphs
Article first published online: 11 SEP 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
How to Cite
McKay, B. D. and Schweitzer, P. (2013), Switching Reconstruction of Digraphs. J. Graph Theory. doi: 10.1002/jgt.21765
- Article first published online: 11 SEP 2013
- Manuscript Revised: 5 AUG 2013
- Manuscript Received: 1 OCT 2012
- Australian Research Council. Grant Number: DP1093320
- Fonds National de la Recherche. Grant Number: FP7-COFUND
- oriented graph;
Switching about a vertex in a digraph means to reverse the direction of every edge incident with that vertex. Bondy and Mercier introduced the problem of whether a digraph can be reconstructed up to isomorphism from the multiset of isomorphism types of digraphs obtained by switching about each vertex. Since the largest known nonreconstructible oriented graphs have eight vertices, it is natural to ask whether there are any larger nonreconstructible graphs. In this article, we continue the investigation of this question. We find that there are exactly 44 nonreconstructible oriented graphs whose underlying undirected graphs have maximum degree at most 2. We also determine the full set of switching-stable oriented graphs, which are those graphs for which all switchings return a digraph isomorphic to the original.