Geodesic
Automorphism groups of a graph and a vertex-deleted subgraph
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl arXiv
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.
DOI : 10.37236/406
Classification : 05C25, 20B25
Mots-clés : automorphism group, reconstruction, Cayley graph, isomorph-free generation 
Stephen G. Hartke; Hannah Kolb; Jared Nishikawa; Derrick Stolee. Automorphism groups of a graph and a vertex-deleted subgraph. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/406
@article{10_37236_406,
     author = {Stephen G. Hartke and Hannah Kolb and Jared Nishikawa and Derrick Stolee},
     title = {Automorphism groups of a graph and a vertex-deleted subgraph},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/406},
     zbl = {1277.05082},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/406/}
}
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