Induced Embeddings of Graphs into Abelian Cayley Graphs

For a finite graph $G$ on $n$ vertices, let $η(G)$ denote the least order of a finite abelian group $Γ$ for which $G$ is an induced subgraph of some Cayley graph of $Γ$. Babai and Sós (1985) settled the worst-case order of magnitude: it is $Θ(n^2)$. We treat $η$ instead as an invariant of the indivi