Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On distance matrices of helm graphs obtained from wheel graphs with an
  even number of vertices   Let $n \geq 4$. The helm graph $H_n$ on $2n-1$ vertices is obtained from the
wheel graph $W_n$ by adjoining a pendant edge to each vertex of the outer cycle
of $W_n$. Suppose $n$ is even. Let $D := [d_{ij}]$ be the distance matrix of
$H_n$. In this paper, we first show that $\det(D) = 3(n-1)2^{n-1}.$ Next, we
find a matrix $\L$ and a vector $u$ such that \[D^{-1} =
-\frac{1}{2}\L+\frac{4}{3(n-1)}uu'.\] We also prove an interlacing property
between the eigenvalues of $\L$ and $D$.

13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn