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Let G be a nonempty simple graph with vertex set V(G) and an edge E(G). For every injective labeling f:V(G)?Z, there are two induced labelings, namely f+:E(G)?Z defined by f+(uv)=f(u)+f(v), f?:E(G)?Z f?(uv)=|f(u)?f(v)|. The sum index the difference minimum cardinalities of ranges f+ f?, respectively. We provide upper lower bounds on index, determine various families graphs. also interesting con...