Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a new extension of the zero-divisor graph   In this paper, we introduce a new graph whose vertices are the nonzero
zero-divisors of commutative ring $R$ and for distincts elements $x$ and $y$ in
the set $Z(R)^{\star}$ of the nonzero zero-divisors of $R$, $x$ and $y$ are
adjacent if and only if $xy=0$ or $x+y\in Z(R)$. we present some properties and
examples of this graph and we study his relation with the zero-divisor graph
and with a subgraph of total graph of a commutative ring.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys