The edit distance function of a hereditary property $\mathscr{ H}$ is the asymptotically largest edit distance between a graph of density $p\in[0,1]$ and $\mathscr{ H}$. Denote by $P_n$ and $C_n$ the path graph of order $n$ and the cycle graph of order $n$, respectively. Let $C_{ 2n}^*$ be the cycle graph $C_{ 2n}$ with a diagonal, and $\widetilde{ C_n}$ be the graph with vertex set $\{ v_0, v_1, \ldots, v_{ n-1}\}$ and $E(\widetilde{ C_n})=E(C_n)\cup \{ v_0v_2\}$. Marchant and Thomason determined the edit distance function of $C_6^{ *}$. Peck studied the edit distance function of $C_n$, while Berikkyzy et al. studied the edit distance of powers of cycles. In this paper, by using the methods of Peck and Martin, we determine the edit distance function of $C_8^{ *}$, $\widetilde{ C_n}$ and $P_n$, respectively.
Categories: math.CO