For two given graphs G1\documentclass[12pt]{minimal}
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\begin{document}$$G_1$$\end{document} and G2\documentclass[12pt]{minimal}
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\begin{document}$$G_2$$\end{document}, the Ramsey number R(G1,G2)\documentclass[12pt]{minimal}
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\begin{document}$$R(G_1,G_2)$$\end{document} is the smallest integer n such that for any graph G of order n, either G contains G1\documentclass[12pt]{minimal}
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\begin{document}$$G_1$$\end{document} or G¯\documentclass[12pt]{minimal}
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\begin{document}$${\overline{G}}$$\end{document} contains G2\documentclass[12pt]{minimal}
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\begin{document}$$G_2$$\end{document}. Let Tn\documentclass[12pt]{minimal}
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\begin{document}$$T_n$$\end{document} denote a tree of order n, and a generalized wheel Ks+Cm\documentclass[12pt]{minimal}
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\begin{document}$$K_s + C_m$$\end{document} is the graph obtained by joining each vertex of Ks\documentclass[12pt]{minimal}
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\begin{document}$$K_s$$\end{document} to each vertex of Cm\documentclass[12pt]{minimal}
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\begin{document}$$C_m$$\end{document}. In this paper, we show that: R(Tn,Ks+C6)=(s+1)(n-1)+1\documentclass[12pt]{minimal}
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\begin{document}$$R(T_n,K_s+ C_6)=(s+1)(n-1)+1$$\end{document} for s≥2\documentclass[12pt]{minimal}
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\begin{document}$$s\ge 2$$\end{document} and n≥5\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 5$$\end{document}, and R(Tn,Ks+C7)=(s+2)(n-1)+1\documentclass[12pt]{minimal}
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\begin{document}$$R(T_n,K_s+ C_7)=(s+2)(n-1)+1$$\end{document} for s≥1\documentclass[12pt]{minimal}
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\begin{document}$$s\ge 1$$\end{document} and n≥5\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 5$$\end{document}.
