Ratio of Symmetries Between any two n-Node Graphs
Abstract
Given any two graphs on the same vertex set, $G_1 = (V, E_1)$ and $G_2 = (V, E_2)$, along with the difference between the two graphs $\Delta = (E_1 \setminus E_2) \cup (E_2 \setminus E_1)$, we prove that the ratio of the sizes of the two graphs' automorphism groups is equivalent to the ratio of the sizes of $\Delta$'s automorphism orbits in $G_1$ and $G_2$ respectively. This result provides a link between graphs' symmetries that might otherwise seem to be unrelated.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2022
- DOI:
- 10.48550/arXiv.2205.05726
- arXiv:
- arXiv:2205.05726
- Bibcode:
- 2022arXiv220505726I
- Keywords:
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- Mathematics - Combinatorics