The Ramsey Numbers of Trees Versus Generalized 6-Wheels or Generalized 7-Wheels

For two given graphs G(1) and G(2), the Ramsey number R(G(1), G(2)) is the smallest integer n such that for any graph G of order n, either G contains G(1) or (G) over bar contains G(2). Let T-n denote a tree of order n, and a generalized wheel K-s + C-m is the graph obtained by joining each vertex of & to each vertex of C-m. In this paper, we show that: R(T-n, K-s + C-6) = (s + 1)(n - 1) + 1 for s >= 2 and n >= 5, and R(T-n, K-s + C-7) = (s + 2)(n - 1) + 1 for s >= 1 and n >= 5.