Automorphism Groups and Adversarial Vertex Deletions

Details Automorphism Groups and Adversarial Vertex Deletions Automorphism Groups and Adversarial Vertex Deletions

2012-01-20

arxiv.org/abs/1201.4367v1

Mathematics

Combinatorics

3 pages

Scientific paper

Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the automorphism group of a graph and a vertex-deleted subgraph. In this note, we provide a construction for a generalized scenario: A list of finite groups is fixed and a graph is provided with automorphism group isomorphic to the first group. Then, an adversary selects an ordering of the remaining groups and requests vertices whose iterated deletions create a sequence of graphs with automorphism groups isomorphic to that ordering of groups.

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