Let $G _ { 0 } = \left( S _ { 0 } , A _ { 0 } \right)$ be a particular fixed graph with $s _ { 0 } = s _ { G _ { 0 } }$, $a _ { 0 } = a _ { G _ { 0 } }$, $s_0 \geq 2$, $a_0 \geq 1$. We now assume that $\lim _ { n \rightarrow + \infty } \left( n ^ { \omega _ { 0 } } p _ { n } \right) = + \infty$.\\
Show that $\lim _ { n \rightarrow + \infty } \frac { \mathbf { V } \left( X _ { n } ^ { 0 } \right) } { \left( \mathbf { E } \left( X _ { n } ^ { 0 } \right) \right) ^ { 2 } } = 0$ where $\mathbf { V } \left( X _ { n } ^ { 0 } \right)$ denotes the variance of $X _ { n } ^ { 0 }$.