On the connectivity and superconnected graphs with small diameter
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In this paper, first we prove that any graph G is 2-connected if diam (G)≤ g-1 for even girth g, and for odd girth g and maximum degree $\Delta$ ≤ 2$\delta$-1 where $\delta$ is the minimum degree. Moreover, we prove that any graph G of diameter diam(G) ≤ g-2 satisfies that (i)G is 5-connected for even girth g and $\Delta$ ≤ 2$\delta$-5, and (ii)G is super-k for odd girth g and $\Delta$ ≤ 3$\delta$/2-1.
CitationBalbuena, C.; Marshall, K.; Montejano, L. On the connectivity and superconnected graphs with small diameter. "Discrete applied mathematics", 06 Març 2010, vol. 158, núm. 5, p. 397-403.