Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The g-extra connectivity of the Mycielskian   The $g$-extra connectivity is an important parameter to measure the ability
of tolerance and reliability of interconnection networks. Given a connected
graph $G=(V,E)$ and a non-negative integer $g$, a subset $S\subseteq V$ is
called a $g$-extra cut of $G$ if $G-S$ is disconnected and every component of
$G-S$ has at least $g+1$ vertices. The cardinality of the minimum $g$-extra cut
is defined as the $g$-extra connectivity of $G$, denoted by $\kappa_g(G)$. In a
search for triangle-free graphs with arbitrarily large chromatic numbers,
Mycielski developed a graph transformation that transforms a graph $G$ into a
new graph $\mu(G)$, which is called the Mycielskian of $G$. This paper
investigates the relationship of the g-extra connectivity of the Mycielskian
$\mu(G)$ and the graph $G$, moreover, show that
$\kappa_{2g+1}(\mu(G))=2\kappa_{g}(G)+1$ for $g\geq 1$ and $\kappa_{g}(G)\leq
min\{g+1, \lfloor\frac{n}{2}\rfloor\}$.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg