Abstract: For two graphs $G$ and $H$, the Ramsey number $R(G, H)$ is the smallest integer $n$ such that for any $n$-vertex graph, either it contains $G$ or its complement contains $H$. Let $S_n$ be a star of order $n$ and $W_{s, m}$ be a generalised wheel $K_s \vee C_m$. Previous studies by Wang and Chen (Graphs Comb 35(1):189-193, 2019) and Chng et al. (Discret Math 344(8):112440, 2021) imply that a tree is $W_{s, 4^{-}}$good, $W_{s, 5^{-}}$good, $W_{s, 6}$-good, and $W_{s, 7^{-}}$good for $s \geqslant 2$. In this paper, we study the Ramsey numbers $R\left(S_n, W_{s, 8}\right)$, and our results indicate that trees are not always $W_{s, 8}$-good.

Key words: Ramsey number, Star, Generalised wheel