Let Z2 = {0, 1} and G = (V, E) be a graph. A labeling f : V −→ Z2 induces an edge labeling f ∗ : E −→ Z2 defined by f ∗ (uv) = f(u).f(v). For i ∈ Z2, let vf (i) = v(i) = card{v ∈ V : f(v) = i} and ef (i) = e(i) = card{e ∈ E : f ∗ (e) = i}. A labeling f is said to be vertex-friendly if | v(0)−v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper we completely determine the vertex balance index set of Kn, Km,n, Cn × P2 and Complete binary tree
