Abstract: Let G=(V(G), E(G)) be a simple connected graph with vertex set V(G) and edge set E(G), respectively. A vertex labeling f: V(G)→Z₂ induces an edge labeling f^*: E(G)→Z₂ defined by f^*(v₁v₂)=f(v₁)+f(v₂) for each edge v₁v₂∈E(G). Given the difference between numbers of vertex labeled 1 and 0 is m (m < |V(G)|), the set of differences between numbers of edges labeled 1 and 0 is called the general index set of graph G. The general index sets of cycle, path and C_n×P₂ are determined.