Word-representability of all 5-regular circulant graphs

Establish that every 5-regular circulant graph is word-representable.

Background

The paper proves word-representability for numerous subclasses of 5-regular circulant graphs, including cases handled through colorability, morphisms, and Cartesian-product factorizations. However, these results do not cover the entire class of 5-regular circulant graphs. The authors therefore formulate the universal claim that all such graphs are word-representable as a conjecture.

References

All 5-regular circulant graphs are word-representable.

— On the Word-Representability of 5-Regular Circulant Graphs  (2512.05480 - Roy et al., 5 Dec 2025) in Conjecture, Section 4 (Conclusion and Future Work), Section \ref{con}