%0 Journal Article %T On vertex balance index set of some graphs %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Adiga, Ch. %A Subbaraya, C. K. %A Shrikanth, A. S. %A Sriraj, M. A. %D 2013 %\ 09/01/2013 %V 39 %N 4 %P 627-634 %! On vertex balance index set of some graphs %K Vertex labeling %K Vertex-friendly %K Vertex balance index set %R %X 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 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. %U http://bims.iranjournals.ir/article_434_8a847dac9d4c818761d9e8df959e4b3a.pdf