On WL-rank of Deza Cayley graphs

TL;DR

This paper introduces an infinite family of Deza Cayley graphs with maximum WL-rank, revealing new insights into their algebraic and combinatorial properties, especially their divisibility and integrality.

Contribution

The authors construct a new infinite family of Deza Cayley graphs with WL-rank equal to the number of vertices, advancing understanding of their structure and properties.

Findings

Constructed an infinite family of Deza Cayley graphs with maximum WL-rank

Graphs are divisible design and integral

WL-rank equals the number of vertices in these graphs

Abstract

The WL-rank of a digraph $\Gamma$ is defined to be the rank of the coherent configuration of $\Gamma$. We construct a new infinite family of strictly Deza Cayley graphs for which the WL-rank is equal to the number of vertices. The graphs from this family are divisible design and integral.