Ramsey numbers of large books

A book B n ${B}_{n}$ is a graph which consists of $n$ triangles sharing common edge. In 1978, Rousseau and Sheehan conjectured that the Ramsey number satisfies r ( m , ) ≤ 2 + c $r({B}_{m},{B}_{n})\le \,2(m+n)+c$ for some constant > 0 $c\gt 0$ . this article, we obtain o 2(m+n)+o(n)$ all $m\le n$ large, confirms conjecture asymptotically. As corollary, our result implies related Faudree, on strongly regular holds