The Cyclic Edge-Connectivity of Strongly Regular Graphs

Abstract

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 $$K_{3,3}$$ ) of degree $$k\ge 3$$ 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 $$K_{2,2,2,2}$$ 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.