For given simple graphs H1,H2,…,Ht\documentclass[12pt]{minimal}
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\begin{document}$$H_1,H_2,\ldots ,H_t$$\end{document}, the Ramsey number R(H1,H2,…,Ht)\documentclass[12pt]{minimal}
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\begin{document}$$R(H_1,H_2,\ldots ,H_t)$$\end{document}, which is often called multi-color Ramsey number, is the smallest integer n such that for an arbitrary decomposition {Gi}i=1t\documentclass[12pt]{minimal}
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\begin{document}$$\{G_i\}_{i=1}^t$$\end{document} of the complete graph Kn\documentclass[12pt]{minimal}
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\begin{document}$$K_n$$\end{document}, there is at least one Gi\documentclass[12pt]{minimal}
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\begin{document}$$G_i$$\end{document} has a subgraph isomorphic to Hi\documentclass[12pt]{minimal}
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\begin{document}$$H_i$$\end{document}. Let m,n1,n2,…,nt\documentclass[12pt]{minimal}
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\begin{document}$$m,n_1,n_2,\ldots , n_t$$\end{document} be positive integers and Σ=∑i=1t(ni-1)\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma =\sum _{i=1}^t(n_i-1)$$\end{document}. Raeisi and Zaghian obtained the R(K1,n1,…,K1,nt,Cm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},C_m)$$\end{document} and R(K1,n1,…,K1,nt,Wm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},W_m)$$\end{document} for odd m≤Σ+2\documentclass[12pt]{minimal}
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\begin{document}$$m\le \Sigma +2$$\end{document}. In this paper, we establish R(K1,n1,…,K1,nt,Wm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},W_m)$$\end{document} for odd m≥Σ+3\documentclass[12pt]{minimal}
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\begin{document}$$m\ge \Sigma +3$$\end{document} and even m≥2Σ+2\documentclass[12pt]{minimal}
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\begin{document}$$m\ge 2\Sigma +2$$\end{document}. We also determine the rest values of R(K1,n1,…,K1,nt,Cm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},C_m)$$\end{document} except for even m≤Σ+1\documentclass[12pt]{minimal}
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\begin{document}$$m\le \Sigma +1$$\end{document} and R(K1,n1,…,K1,nt,Pm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},P_m)$$\end{document} for m≥Σ+1\documentclass[12pt]{minimal}
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\begin{document}$$m\ge \Sigma +1$$\end{document}, or m≤Σ\documentclass[12pt]{minimal}
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\begin{document}$$m\le \Sigma $$\end{document} and Σ≡0,1(modm-1)\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma \equiv 0,1(\text{ mod }\, m-1)$$\end{document}, which extends a result on R(K1,n1,…,K1,nt,Pm)\documentclass[12pt]{minimal}
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\begin{document}$$R(K_{1,n_1},\ldots ,K_{1,n_t},P_m)$$\end{document} obtained by K. Zhang and S. Zhang.
