The Cyclic Edge-Connectivity of Strongly Regular Graphs

Let G be a connected graph. An edge cut set M of G is a cyclic edge cut set if there are at least two components of G - M which contain a cycle. The cyclic edge-connectivity of G is the minimum cardinality of a cyclic edge cut set (if exists) of G. In this paper, we show that the cyclic edge-connectivity of a connected strongly regular graph G (not K-3,K-3) of degree k >= 3 with girth c is equal to (k - 2)c, where c = 3, 4 or 5. Moreover, if G is not the triangular graph srg-(10, 6, 3, 4), the complete multi-partite graph K-2,K-2,K-2,K-2 or the lattice graph srg-(16, 6, 2, 2), then each cyclic edge cut set of size (k - 2)c is precisely the set of edges incident with a cycle of length c in G.