# Girth of petersen graph

Why Girth of petersen graph is not 4? here is my graph-:

Here 2 element subset $\left(i,j\right)$, $i,j$ belongs to ${1,2,3,4,5}$ ,is disjoint to each other.

This is not a cycle, it's traversing the same edge back and forth. You could use the same approach to say that the girth is actually 2! Just walk from $(1,2)$ to $(3,4)$ and back...