Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eccentricity energy change of complete multipartite graphs due to edge
  deletion   The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is obtained from the
distance matrix of $G$ by retaining the largest distances in each row and each
column, and leaving zeros in the remaining ones. The eccentricity energy of $G$
is sum of the absolute values of the eigenvalues of $\varepsilon(G)$. Although
the eccentricity matrices of graphs are closely related to the distance
matrices of graphs, a number of properties of eccentricity matrices are
substantially different from those of the distance matrices. The change in
eccentricity energy of a graph due to an edge deletion is one such property. In
this article, we give examples of graphs for which the eccentricity energy
increase (resp., decrease) but the distance energy decrease (resp., increase)
due to an edge deletion. Also, we prove that the eccentricity energy of the
complete $k$-partite graph $K_{n_1,\hdots,n_k}$ with $k\geq 2$ and $ n_i\geq
2$, increases due to an edge deletion.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga