discrete

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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
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