The Ramsey numbers for stars of even order versus a wheel of order nine

For two given graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest positive integer n such that for any graph G of order n , either G contains G 1 or the complement of G contains G 2 . Let S n denote a star of order n and W m a wheel of order m + 1 . In this paper, we show that R ( S n , W 8 ) = 2 n + 2 for n ≥ 6 and n ≡ 0 ( mod 2 ) .