Superconnectivity of graphs with odd girth gg and even girth hh

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