A lower bound for the Weisfeiler-Leman dimension of circulant graphs

TL;DR

This paper establishes a lower bound on the Weisfeiler-Leman dimension for infinitely many circulant graphs, showing it grows at least proportionally to the square root of the logarithm of their order.

Contribution

It proves that infinitely many circulant graphs have Weisfeiler-Leman dimension at least c√log n, providing new insights into graph isomorphism complexity.

Findings

Weisfeiler-Leman dimension can grow at least as c√log n for certain circulant graphs.

The result applies to infinitely many graph orders n.

It advances understanding of graph isomorphism testing limitations.

Abstract

It is proved that for infinitely many positive integers n, there exists a circulant graph of order n whose Weisfeiler-Leman dimension is at least c\sqrt{log n} for some positive constant c not depending on n.