%0 Journal Article
%T Automorphism groups of a graph and a vertex-deleted subgraph
%A Stephen G. Hartke
%A Hannah Kolb
%A Jared Nishikawa
%A Derrick Stolee
%J Mathematics
%D 2009
%I arXiv
%X Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question of which pairs of groups can be represented as the automorphism groups of a graph and a vertex-deleted subgraph. This, and more surprisingly the analogous question for edge-deleted subgraphs, are answered in the most positive sense using concrete constructions.
%U http://arxiv.org/abs/0909.3252v1