Graphs with small diameter determined by their $D$-spectra

Liu, Ruifang, and Xue, Jie. "Graphs with small diameter determined by their $D$-spectra." Czechoslovak Mathematical Journal 68.1 (2018): 1-17. <http://eudml.org/doc/294696>.

@article{Liu2018,
abstract = {Let $G$ be a connected graph with vertex set $V(G)=\lbrace v_\{1\},v_\{2\},\ldots ,v_\{n\}\rbrace $. The distance matrix $D(G)=(d_\{ij\})_\{n\times n\}$ is the matrix indexed by the vertices of $G$, where $d_\{ij\}$ denotes the distance between the vertices $v_\{i\}$ and $v_\{j\}$. Suppose that $\lambda _\{1\}(D)\ge \lambda _\{2\}(D)\ge \cdots \ge \lambda _\{n\}(D)$ are the distance spectrum of $G$. The graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph having the same spectrum as $G$ is isomorphic to $G$. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their $D$-spectra.},
author = {Liu, Ruifang, Xue, Jie},
journal = {Czechoslovak Mathematical Journal},
keywords = {distance spectrum; distance characteristic polynomial; $D$-spectrum determined by its $D$-spectrum},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Graphs with small diameter determined by their $D$-spectra},
url = {http://eudml.org/doc/294696},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Liu, Ruifang
AU - Xue, Jie
TI - Graphs with small diameter determined by their $D$-spectra
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 1
EP - 17
AB - Let $G$ be a connected graph with vertex set $V(G)=\lbrace v_{1},v_{2},\ldots ,v_{n}\rbrace $. The distance matrix $D(G)=(d_{ij})_{n\times n}$ is the matrix indexed by the vertices of $G$, where $d_{ij}$ denotes the distance between the vertices $v_{i}$ and $v_{j}$. Suppose that $\lambda _{1}(D)\ge \lambda _{2}(D)\ge \cdots \ge \lambda _{n}(D)$ are the distance spectrum of $G$. The graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D(G)$, any graph having the same spectrum as $G$ is isomorphic to $G$. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined by their $D$-spectra.
LA - eng
KW - distance spectrum; distance characteristic polynomial; $D$-spectrum determined by its $D$-spectrum
UR - http://eudml.org/doc/294696
ER -