Distance spectrum; Complement; Cospectral.
Let $G$ be a connected graph with order $n$. Let $\lambda_1(D(G))\geq \cdots\geq \lambda_n(D(G))$ be the distance spectrum of $G$. In this paper, it is shown that the complements of $P_n$ and $C_n$ are determined by their $D$-spectrum. Moreover, it is shown that the cycle $C_n$ ($n$ odd) is also determined by its $D$-spectrum.
Drury, Stephen and Lin, Huiqiu.
"Some Graphs Determined By Their Distance Spectrum",
Electronic Journal of Linear Algebra,
Volume 34, pp. 320-330.