On the connectivity and superconnected graphs with small diameter ?
In this paper, first we prove that any graph G G is 2-connected if diam(G)?g?1 d i a m ( G ) ? g ? 1 for even girth g g , and for odd girth g g and maximum degree ??2??1 ? ? 2 ? ? 1 where ? ? is the minimum degree. Moreover, we prove that any graph G G of diameter diam(G)?g?2 d i a m ( G ) ? g ? 2 satisfies that (i) G G is 5-connected for even girth g g and ??2??5 ? ? 2 ? ? 5 , and (ii) G G is super-? ? for odd girth g g and ??3?/2?1 ? ? 3 ? / 2 ? 1 .
connectivity superconnected diameter girth