Abstract
We prove that for any graphG the edge-deleted subgraphs ofG partition into two isomorphism classes if and only if the edges ofG partition into two orbits under the automorphism group ofG.
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Andersen, L.D., Ding, S., Sabidussi, G. et al. Edge orbits and edge-deleted subgraphs. Graphs and Combinatorics 8, 31–44 (1992). https://doi.org/10.1007/BF01271706
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DOI: https://doi.org/10.1007/BF01271706