Geodesic
The EKR-module property of pseudo-Paley graphs of square order
Shamil Asgarli1 ; Sergey Goryainov2 ; Huiqiu Lin3 ; Chi Hoi Yip1
1University of British Columbia
2Hebei Normal University
3East China University of Science and Technology
The electronic journal of combinatorics, Tome 29 (2022) no. 4
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We prove that a family of pseudo-Paley graphs of square order obtained from unions of cyclotomic classes satisfies the Erdős-Ko-Rado (EKR) module property, in a sense that the characteristic vector of each maximum clique is a linear combination of characteristic vectors of canonical cliques. This extends the EKR-module property of Paley graphs of square order and solves a problem proposed by Godsil and Meagher. Different from previous works, which heavily rely on tools from number theory, our approach is purely combinatorial in nature. The main strategy is to view these graphs as block graphs of orthogonal arrays, which is of independent interest.
DOI : 10.37236/10962
Classification : 05D05, 05C25, 05B15, 05C69, 05C75, 05C35
Mots-clés : strict-EKR property, Cayley graph, Peisert-type graphs

Shamil Asgarli  1   ; Sergey Goryainov  2   ; Huiqiu Lin  3   ; Chi Hoi Yip  1

1 University of British Columbia
2 Hebei Normal University
3 East China University of Science and Technology 
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     title = {The {EKR-module} property of {pseudo-Paley} graphs of square order},
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Shamil  Asgarli; Sergey Goryainov; Huiqiu Lin; Chi Hoi Yip. The EKR-module property of pseudo-Paley graphs of square order. The electronic journal of combinatorics, Tome 29 (2022) no. 4. doi: 10.37236/10962

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