Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Wiener index, distance cospectrality and transmission regular
  graphs   In this paper, we investigate various algebraic and graph theoretic
properties of the distance matrix of a graph. Two graphs are $D$-cospectral if
their distance matrices have the same spectrum. We construct infinite pairs of
$D$-cospectral graphs with different diameter and different Wiener index. A
graph is $k$-transmission-regular if its distance matrix has constant row sum
equal to $k$. We establish tight upper and lower bounds for the row sum of a
$k$-transmission-regular graph in terms of the number of vertices of the graph.
Finally, we determine the Wiener index and its complexity for linear $k$-trees,
and obtain a closed form for the Wiener index of block-clique graphs in terms
of the Laplacian eigenvalues of the graph. The latter leads to a generalization
of a result for trees which was proved independently by Mohar and Merris.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an