Automorphism groups of a graph and a vertex-deleted subgraph

Stephen G. Hartke, Hannah Kolb, Jared Nishikawa, Derrick Stolee

Published 2009-09-17Version 1

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.