On the Ramsey number of the quadrilateral versus the book and the wheel

Let G and H be graphs. The Ramsey number R(G, H) is the least integer such that for every graph F of order R(G, H), either F contains G or F contains H . Let Bn and Wn denote the book graph K2 +Kn and the wheel graph K1 + Cn−1, respectively. In 1978, Faudree, Rousseau and Sheehan computed R(C4, Bn) for n ≤ 8. In this paper, we compute R(C4, Bn) for 8 ≤ n ≤ 12 and R(C4, Wn) for 4 ≤ n ≤ 13. In particular, we find that R(C4, B8) = 17, not 16 as claimed in 1978 by Faudree, Rousseau and Sheehan. Most of the results are based on computer algorithms.