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] most recent 30 from http://mathoverflow.net 2013-05-25T18:02:11Z http://mathoverflow.net/feeds/question/96964 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96964/if-g-is-2-self-centered-graph-then-how-to-prove-that-g-has-at-least-2n If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$ saina 2012-05-15T04:45:42Z 2012-05-15T04:45:42Z <p>If $G$ is 2 - self centered graph. then how to prove that $G$ has at least $2n - 5$ edges? where $n\geq 5$.</p> <p>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</p> <p>$\mid E\mid\geq \frac{3n}{2}>2n-5$ (I am stucked here. How to prove this. Sincerely thanks for giving me time.)</p>