If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$

2012-05-15T04:45:42Z

If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$.

I started by assuming if number of edges $\mid E\mid\leq 2n-6$ then there exist a vertex say $u$ such that $deg = 2$ otherwise if no such vertex exists then

$\mid E\mid\geq \frac{3n}{2}>2n-5$ (I am stucked here. How to prove this. Sincerely thanks for giving me time.)

If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$ - MathOverflow [closed]

If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$