Tightness of the established upper bounds

Determine whether the upper bounds established for fixed graph powers, line graphs, and clique-sums are tight.

Background

The paper proves preservation and quantitative upper bounds for strong isometric path complexity under fixed powers, line graphs, and clique-sums. The conclusion explicitly states that the tightness of these bounds is unresolved, leaving open the task of identifying matching constructions or improving the estimates.

References

However, it is not clear if our upper bounds are tight.

— Strong isometric path complexity of graphs: Asymptotic minors, restricted holes, and graph operations  (2501.10828 - Chakraborty et al., 18 Jan 2025) in Section 6, Conclusion