Abstract
Girth pairs were introduced by Harary and Kovács [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209–218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then ( g , h ) is called the girth pair of the graph. In this paper we prove that a graph with girth pair ( g , h ) such that g is odd and h ⩾ g + 3 is even has high (vertex-)connectivity if its diameter is at most h - 3 . The edge version of all results is also studied.
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