ALGEBRAIC COMBINATORICS

no. 4
Maximality of subfields as cliques in Cayley graphs over finite fields
Yip, Chi Hoi1
1 Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver V6T 1Z2 Canada
Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 901-905.

We show the maximality of subfields as cliques in a special family of Cayley graphs defined on the additive group of a finite field. In particular, this confirms a conjecture of Yip on generalized Paley graphs.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.291
Classification: 05C25, 05C69, 11T24
Keywords: Cayley graph, maximal clique, character sum
Yip, Chi Hoi 1

1 Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver V6T 1Z2 Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yip, Chi Hoi. Maximality of subfields as cliques in Cayley graphs over finite fields. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 901-905. doi : 10.5802/alco.291. https://alco.centre-mersenne.org/articles/10.5802/alco.291/

[1] Asgarli, Shamil; Yip, Chi Hoi Van Lint–MacWilliams’ conjecture and maximum cliques in Cayley graphs over finite fields, J. Combin. Theory Ser. A, Volume 192 (2022), Paper no. 105667, 23 pages | MR | Zbl

[2] Blokhuis, A. On subsets of GF (q 2 ) with square differences, Nederl. Akad. Wetensch. Indag. Math., Volume 46 (1984) no. 4, pp. 369-372 | DOI | MR | Zbl

[3] Broere, I.; Döman, D.; Ridley, J. N. The clique numbers and chromatic numbers of certain Paley graphs, Quaestiones Math., Volume 11 (1988) no. 1, pp. 91-93 | DOI | MR | Zbl

[4] Cohen, Stephen D. Clique numbers of Paley graphs, Quaestiones Math., Volume 11 (1988) no. 2, pp. 225-231 | DOI | MR | Zbl

[5] Croot, Ernest S. III; Lev, Vsevolod F. Open problems in additive combinatorics, Additive combinatorics (CRM Proc. Lecture Notes), Volume 43, Amer. Math. Soc., Providence, RI, 2007, pp. 207-233 | DOI | MR | Zbl

[6] Green, Ben Counting sets with small sumset, and the clique number of random Cayley graphs, Combinatorica, Volume 25 (2005) no. 3, pp. 307-326 | DOI | MR | Zbl

[7] Katz, Nicholas M. An estimate for character sums, J. Amer. Math. Soc., Volume 2 (1989) no. 2, pp. 197-200 | DOI | MR | Zbl

[8] Lidl, Rudolf; Niederreiter, Harald Finite fields, Encyclopedia of Mathematics and its Applications, 20, Cambridge University Press, Cambridge, 1997, xiv+755 pages (With a foreword by P. M. Cohn)

[9] Mullin, Natalie Self-complementary arc-transitive graphs and their imposters (2009) https://uwspace.uwaterloo.ca/handle/10012/4264 (Master’s thesis, University of Waterloo)

[10] Peisert, Wojciech All self-complementary symmetric graphs, J. Algebra, Volume 240 (2001) no. 1, pp. 209-229 | DOI | MR | Zbl

[11] Yip, Chi Hoi Gauss sums and the maximum cliques in generalized Paley graphs of square order, Funct. Approx. Comment. Math., Volume 66 (2022) no. 1, pp. 119-138 | MR | Zbl

[12] Yip, Chi Hoi On maximal cliques of Cayley graphs over fields, J. Algebraic Combin., Volume 56 (2022) no. 2, pp. 323-333 | MR | Zbl

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