Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X39420130901On vertex balance index set of some graphs627634434ENCh.AdigaUniversity of MysoreC. K.SubbarayaAdichunchanagiri Institute of TechnologyA. S.ShrikanthUniversity of MysoreM. A.SrirajUniversity of MysoreJournal Article20110111Let 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 ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε 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.http://bims.iranjournals.ir/article_434_8a847dac9d4c818761d9e8df959e4b3a.pdf