Ratio of Symmetries Between any two nNode 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:

arXiv eprints
 Pub Date:
 May 2022
 DOI:
 10.48550/arXiv.2205.05726
 arXiv:
 arXiv:2205.05726
 Bibcode:
 2022arXiv220505726I
 Keywords:

 Mathematics  Combinatorics