On Edge-Balance Index Sets of the Graph Cn×Pb(n=0,1,2mod6)

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z2=(0,1) For a given binary edge labeling f:E(G)→Z2,the edge labeling f induces a partial vertex labeling f*:V(G)→Z2 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 , otherwise f*(v) is undefined. For i∈Z2, let v(i)=card(e∈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 } . In this paper, we completely determine the edge-balance index |e(0)-e(1)|≤1 sets of the graph Cn×Pb(n=0,1,2 mod 6)