Ramsey numbers for trees II

Let $r(G_1,G_2)$ be the Ramsey number of the two graphs $G_1$ and $G_2$. For $n_1\ge n_2\ge 1$ let $S(n_1,n_2)$ be the double star given by $V(S(n_1,n_2))=\{v_0,v_1,\dots ,v_{n_1},w_0,w_1,\dots ,w_{n_2}\}$ and $E(S(n_1,n_2))=\{v_0{v}_1,\dots ,v_0{v}_{n_1},v_0{w}_0,w_0{w}_1,\dots ,w_0{w}_{n_2}\}$. In this paper we determine $r(K_{1,m-1},$ $S(n_1,n_2))$ under certain conditions. For $n\ge 6$ let $T_n^3=S(n-5,3)$, $T_n^{{}^{\mathrm{\prime }\mathrm{\prime }}}=(V,E_2)$ and $T_n^{{}^{\mathrm{\prime }\mathrm{\prime }\mathrm{\prime }}}=(V,E_3)$, where $V=\{v_0,v_1,\dots ,v_{n-1}\}$, $E_2=\{v_0{v}_1,\dots ,v_0{v}_{n-4},v_1{v}_{n-3},v_1{v}_{n-2},$ $v_2{v}_{n-1}\}$ and $E_3=\{v_0{v}_1,\dots ,v_0{v}_{n-4},v_1{v}_{n-3},v_2{v}_{n-2},v_3{v}_{n-1}\}$. We also obtain explicit formulas for $r$ $(K_{1,m-1},T_n)$, $r(T_m^{\mathrm{\prime }},T_n)$ $(n\ge m+3)$, $r(T_n,T_n)$, $r(T_n^{\mathrm{\prime }},T_n)$ and $r(P_n,T_n)$, where $T_n\in \{T_n^{\mathrm{\prime }\mathrm{\prime }},T_n^{\mathrm{\prime }\mathrm{\prime }\mathrm{\prime }},T_n^3\}$, $P_n$ is the path on $n$ vertices and $T_n^{\mathrm{\prime }}$ is the unique tree with $n$ vertices and maximal degree $n-2$.