Monophonic position number of circulant graphs

Construct, for every \(n\geq11\), a circulant graph of order \(n\), monophonic position number 2, and diameter 2.

Background

The survey describes a conjecture motivated by computations and constructions of graphs with monophonic position number 2 and diameter 2. The conjecture asserts that circulant examples exist at every order at least 11.

References

For any $n \geq 11$, there is a circulant graph with order $n$, monophonic position number $a = 2$ and diameter $D = 2$.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 5, subsection “Monophonic position sets”