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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.)

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    Also posted to mathoverflow.net, where it ought to be closed sometime soon. So: what's a 2-self centered graph?2012-05-15
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    It probably means a self-centered graph (diameter=radius) of radius 2.2012-05-15
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    Since there are 2-self-centered graphs of arbitrarily large n, you will not be able to prove $\frac{3n}{2} \gt 2n-5$.2012-05-16

2 Answers 2