Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree polynomial of vertices in a graph and its behavior under graph
  operations   In this paper, we introduce a new concept namely degree polynomial for
vertices of a simple graph. This notion leads to a concept namely degree
polynomial sequence which is stronger than the concept of degree sequence.
After obtaining the degree polynomial sequence for some well-known graphs, we
prove a theorem which gives a necessary condition for realizability of a
sequence of polynomials with coefficients in positive integers. Also we
calculate the degree polynomial for vertises of join, Cartesian product, tensor
product, and lexicographic product of two simple graphs and for vertices of the
complement of a simple graph. Some examples, counterexamples, and open problems
concerning to this subjects, is given as well

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga