The Ramsey Number for Copies Some Tree Versus Whell and Complete Graphs

Abstract. For given graphs G and H, the Ramsey number R(G,H)\ud is the smallest natural number n such that for every graph F of order\ud n: either F contains G or the complement of F contains H. This paper\ud investigates the Ramsey number R([G,H), where G contains tree and\ud H are wheel Wm and complete graph Km. We show that if n is even\ud and n 3, then R(2Sn,W4) = 3n. Furthermore, if n 3 and m is odd,\ud m 2n ??? 1, then R(kSn,Wm) = 3n ??? 2 + (k ??? 1)n, and for arbitrary n\ud and m, then R(\ud Sk\ud i=1 Tni ,Km) = R(Tnk ,Km) +\ud Pk???1\ud i=1 ni