Enumeration of strictly Deza graphs with at most 21 vertices

Goryainov, Sergey; Panasenko, Dmitry; Shalaginov, Leonid

doi:10.48550/arxiv.2102.10624

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2021

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“…All strictly Deza circulants of WL-rank 4 were classified in [3]. Some constructions of strictly Deza graphs of WL-rank 4 were suggested in [14].…”

Section: Introductionmentioning

confidence: 99%

On WL-rank and WL-dimension of some Deza dihedrants

Ryabov¹,

Shalaginov²

2021

Preprint

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The WL-rank of a graph Γ is defined to be the rank of the coherent configuration of Γ. The WL-dimension of Γ is defined to be the smallest positive integer m for which Γ is identified by the m-dimensional Weisfeiler-Leman algorithm. We establish that some families of strictly Deza dihedrants have WL-rank 4 or 5 and WL-dimension 2. Computer calculations imply that every strictly Deza dihedrant with at most 59 vertices is circulant or belongs to one of the above families. We also construct a new infinite family of strictly Deza dihedrants whose WL-rank is a linear function of the number of vertices.

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“…All strictly Deza circulants of WL-rank 4 were classified in [3]. Some constructions of strictly Deza graphs of WL-rank 4 were suggested in [14].…”

Section: Introductionmentioning

confidence: 99%