Let G be a connected 3 - regular graph. Each edge of G lies on some cycle. Let S⊆V and C1,C2,…,Cm,m=Codd(G−S), be the odd component of G−S. Let eG(Ci,S) denote the number of edges with one- end in Ci and the other in S. Then
∑(i=1 to m) eG(Ci−S) is
(1) ≤m
(2) ≥5m
(3) ≥3m
