λ′-optimal regular graphs with two orbits

An edge set F is called a restricted edge-cut if G-F is disconnected and contains no isolated vertices. The minimum cardinality over all restricted edge-cuts is called restricted edge-connectivity of G, and denoted by lambda'(G). A graph G is called lambda'-optimal if lambda'(G) = zeta(G), where zeta(G) = min{d(G)(u) + d(G)(v) 2 : uv is an element of E(C)}. In this note, we obtain a sufficient condition for a k(>= 3)-regular connected graph with two orbits to be lambda'-optimal.