FULL EDGE-FRIENDLY INDEX SETS OF COMPLETE BIPARTITE GRAPHS

Let G = (V;E) be a simple graph. An edge labeling f : E ! f0; 1g induces a vertex labeling f+ : V ! Z2 dened by f+(v) Σ uv2E f(uv) (mod 2) for each v 2 V , where Z2 = f0; 1g is the additive group of order 2. For i 2 f0; 1g, let ef (i) = jf -1(i)j and vf (i) = j(f+) -1(i)j. A labeling f is called edge-friendly if jef (1) - ef (0)j 1. If (G) = vf (1) - vf (0) is called the edge-friendly index of G under an edge-friendly labeling f. The full edge-friendly index set of a graph G is the set of all possible edge-friendly indices of G. Full edge-friendly index sets of complete bipartite graphs will be determined.