Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs with small diameter determined by their $D$-spectra   Let $G$ be a connected graph with vertex set
$V(G)=\{v_{1},v_{2},...,v_{n}\}$. 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
$\lambda_{1}(D)\geq\lambda_{2}(D)\geq\cdots\geq\lambda_{n}(D)$ 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 $G$. In this paper, we give the distance characteristic
polynomial of some graphs with small diameter, and also prove that these graphs
are determined by their $D$-spectra.

9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics