THE RAMSEY NUMBERS FOR STARS OF ODD ORDER VERSUS A WHEEL OF ORDER NINE

For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Sn denote a star of order n and Wm a wheel of order m + 1. In this paper we show that R(Sn, W8) = 2n + 1 for n ≥ 5 and n ≡ 1 (mod 2).