On Superconnectivity of (4, g)-Cages
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A (k, g)-cage is a graph that has the least number of vertices among all k-regular graphs with girth g. It has been conjectured (Fu et al. in J. Graph Theory, 24:187–191, 1997) that all (k, g)-cages are k-connected for every k ≥ 3. A k-connected graph G is called superconnected if every k-cutset S is the neighborhood of some vertex. Moreover, if G−S has precisely two components, then G is called tightly superconnected. In this paper, we prove that every (4, g)-cage is tightly superconnected when g ≥ 11 is odd.
KeywordsCage Superconnected Tightly superconnected
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