The longest induced cycle conjecture for unitary Cayley graphs

Let $X_n$ be the unitary Cayley graph considered in the paper, and let $m(r)$ denote the maximum length of an induced cycle in $X_n$ when the underlying modulus has $r$ distinct prime factors. Longest induced cycle conjecture.

$$m(r)=2^r+2.$$

The conjecture is based on exhaustive computer searches of arrays representing induced cycles and suggests an exact formula for the longest induced cycle. The surrounding discussion also indicates that the result may extend to related conjunctions of complete multipartite graphs, but no proof or resolution is given here.