Switching Reconstruction of Digraphs
Abstract
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 non-reconstructible oriented graphs have 8 vertices, it is natural to ask whether there are any larger non-reconstructible graphs. In this paper we continue the investigation of this question. We find that there are exactly 44 non-reconstructible 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.
Keywords
Cite
@article{arxiv.1308.0675,
title = {Switching Reconstruction of Digraphs},
author = {Brendan D. McKay and Pascal Schweitzer},
journal= {arXiv preprint arXiv:1308.0675},
year = {2013}
}