Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z_{2} = {0,1}. For a given binary edge labeling f :E(G)→Z_{2} , the edge labeling f induces a partial vertex labeling f*:V(G)→Z_{2} such that f*(v) =1(0) iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (1-edges) incident to v , otherwise f*(v) is idefined. For i∈Z_{2} , let v(i)=card{v∈V(G): f*(v) =i} and e(i) = card{e∈E(G) : f (e)=i}. The edge-balance index sets of a graph G,EBI(G), is defined as {|v(0) −v(1) |: the edge labeling f satisfies |e(0)−e(1) |≤1}.In this paper, we completely determine the edge-balance C_{n}xP _{6}(n=3,4,5mod6).
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