A　book　(Formula　presented.)　is　a　graph　which　consists　of　(Formula　presented.)　triangles　sharing　a　common　edge.　In　1978,　Rousseau　and　Sheehan　conjectured　that　the　Ramsey　number　satisfies　(Formula　presented.)　for　some　constant　(Formula　presented.).　In　this　article,　we　obtain　that　(Formula　presented.)　for　all　(Formula　presented.)　and　(Formula　presented.)　large,　which　confirms　the　conjecture　of　Rousseau　and　Sheehan　asymptotically.　As　a　corollary,　our　result　implies　that　a　related　conjecture　of　Faudree,　Rousseau　and　Sheehan　on　strongly　regular　graph　holds　asymptotically.　©　2022　Wiley　Periodicals　LLC.