Consider the following statements:
$\text{P}$: There exists no simple, undirected and connected graph with $80$ vertices and $77$ edges.
$\text{Q}$: All vertices of Euler graph are of even degree.
$\text{R}$: Every simple, undirected, connected and acyclic graph with $50$ vertices has at least two vertices of degree one.
$\mathrm{S}$ : There exits a bipartite graph with more than ten vertices which is $2$-colorable.
What is the number of correct statements among the above statements.
- $1$
- $2$
- $3$
- $4$
(Option $1[39461]) 1$
(Option $2[39462]) 2$
(Option $3[39463]) 3$
(Option $4[39464]) 4$
Answer Given by Candidate: $2$