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For two given graphs \( G \) and \( H \), the Ramsey number \( R(G, H) \) is the smallest positive integer \( N \) such that for every graph \( F \) of order \( N \) the following holds: either \( F \) contains \( G \) as a subgraph or the complement of \( F \) contains \( H \) as a subgraph. In this paper, we shall study the Ramsey number \( R(T_n, W_m) \) for a star-like tree \( T_n \) with \( n \) vertices and a wheel \( W_m \) with \( m + 1 \) vertices and \( m \) odd. We show that the Ramsey number \( R(S_n, W_m) = 3n – 2 \) for \( n \geq 2m – 4, m \geq 5 \) and \( m \) odd, where \( S_n \) denotes the star on \( n \) vertices. We conjecture that the Ramsey number is the same for general trees on \( n \) vertices, and support this conjecture by proving it for a number of star-like trees.