On the Superconnectivity in graphs with odd girth g and even girth h

A maximally connected graph G of minimum degree δ is said to be superconnected (for short super-κ) if all disconnecting sets of cardinality δ are the neighborhood of some vertex of degree δ. Sufficient conditions on the diameter to guarantee that a graph of odd girth g and even girth h⩾g+3 is super-κ are stated. Also polarity graphs are shown to be super-κ.