λc-Optimally half vertex transitive graphs with regularity k

The cyclic edge connectivity λc(G) of a graph G is the minimum number of edges whose removal results in a disconnected graph and every connected component contains cycles. If λc(G) exists, we call G λc-connected. And if λc(G) gets the maximum value, we call G λc-optimal. A bipartite graph is said to be half vertex transitive if its automorphism group is transitive on the sets of its bipartition. In this paper, we show that a connected k(⩾4)-regular half vertex transitive graph G with girth g⩾6 is λc-optimal, and we also obtain a sufficient and necessary condition for a connected k(⩾4)-regular half vertex transitive graph G with girth 4 to be λc-optimal.