Original Articles

THE CLIQUE NUMBERS AND CHROMATIC NUMBERS OF CERTAIN PALEY GRAPHS

Published in: Quaestiones Mathematicae
Volume 11 , issue 1 , 1988 , pages: 91–93

DOI: 10.1080/16073606.1988.9631945

Author(s): I. Broere Department of Mathematics, South Africa , D. Döman Department of Mathematics and Applied Mathematics, South Africa , J.N. Ridley Department of Mathematics, South Africa

Keywords: 05C15 , 12C15

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Abstract

The problem of finding a formula for the clique number of the Paley graph G*(p) where p is a prime number such that p ≡ 1(mod 4) seems to be a hard one. These clique numbers are known for the caws 5 ⋚ p ⋚ 1601. In this paper we show that the clique number and chromatic number of the Paley graph G*(p^2r) are both p^r, where p is an odd prime and r is a natural number. Upper and lower bounds for the clique numbers and chromatic numbers of some related graphs are also determined.

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