The crossing number of chordal ring networks (Q313472)

For an even integer \(n \geq 2\), let \(\mathbb{Z}_n\) denote the set of integers modulo \(n\). Let \(x\), \(y\), \(z\) be distinct odd positive integers in \(\mathbb{Z}_n\). The chordal ring network \(\mathrm{CR}_n(x,y,z)\) has vertex set \(\mathbb{Z}_n\) and for every even \(i \in \mathbb{Z}_n\) vertex \(i\) is adjacent with precisely the three vertices \(i+x\), \(i+y\) and \(i+z\). The authors obtain exact values for the crossing number of \(\mathrm{CR}_n(1,3,9)\) for \(n \in \{10,12, \ldots, 22\}\) and \(n \equiv 0 \pmod 8\) and for all other even values of \(n \geq 26\) the authors determine upper bounds for the crossing number of \(\mathrm{CR}_n(1,3,9)\).