Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neighbor product distinguishing total colorings of corona of subcubic
  graphs   A proper $[k]$-total coloring $c$ of a graph $G$ is a mapping $c$ from
$V(G)\bigcup E(G)$ to $[k]=\{1,2,\cdots,k\}$ such that $c(x)\neq c(y)$ for
which $x$, $y\in V(G)\bigcup E(G)$ and $x$ is adjacent to or incident with $y$.
Let $\prod(v)$ denote the product of $c(v)$ and the colors on all the edges
incident with $v$. For each edge $uv\in E(G)$, if $\prod(u)\neq \prod(v)$, then
the coloring $c$ is called a neighbor product distinguishing total coloring of
$G$. we use $\chi"_{\prod}(G)$ to denote the minimal value of $k$ in such a
coloring of $G$. In 2015, Li et al. conjectured that $\Delta(G)+3$ colors
enable a graph to have a neighbor product distinguishing total coloring. In
this paper, we consider the neighbor product distinguishing total coloring of
corona product $G\circ H$, and obtain that $\chi"_{\prod}(G\circ H)\leq
\Delta(G\circ H)+3$.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn