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Maximal cliques in the Paley graph of square order

✍ Scribed by R.D. Baker; G.L. Ebert; J. Hemmeter; A. Woldar

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
424 KB
Volume
56
Category
Article
ISSN
0378-3758

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✦ Synopsis

Determining the clique number of the Paley graph of order q, 4 E I (mod 4) a prime power, is a difficult problem. However, the work of Blokhuis implies that in the Paley graph of order q2, where q is any odd prime power, the clique number is in fact q. In this paper we construct maximal cliques of size i(q + I) or i(q + 3), accordingly as q s I (mod 4) or q E 3 (mod 4 I. in the Paley graph of order q2. It is believed that these are the largest maximal cliques which are not maximum. We also briefly discuss maximal cliques in some graphs naturally associated with the interior and exterior points of a conic in PG(2,q) for odd prime powers 4.

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