Automorphism Groups of a Graph and a Vertex-Deleted Subgraph

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


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.

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