Restrict Edge-Connectivity of Circular Graphs

An edge cut X of G is restrict if G−X is disconnected and has no trivial component. The minimum k such that G has a restrict k-edge cut is called the restrict edge-connectivity of G. Let n and i1, i2, · · · , ik are positive integers such that n> i1> i2> · · ·> ik. A circular graph G = C(n; i1, i2, · · · , ik) of order n is one graph spanned by a n-cycle Cn = (0, 1, · · · , n, 1) together with the chords (i, j) ∈ E if and only if i+ ik ≡ j(mod n). The cycle Cn is the principal cycle of C(n; i1, i2, · · · , ik). In this paper, we prove that the restrict edge connectivity of C(n, n/2, k) is 8