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

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

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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...

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  • $\begingroup$ but girth can't be 2...as cycle can't be of length 2 $\endgroup$ – virat Oct 31 '16 at 20:30
  • $\begingroup$ Yes, and your example is walking a cycle of length 2 twice. $\endgroup$ – Alon Amit Oct 31 '16 at 20:31

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