full edge-friendly index sets of complete bipartite graphs

‎‎let g=(v,e) be a simple graph‎. ‎an edge labeling f:e→{0,1} induces a vertex labeling f+:v→z2 defined by f+(v)≡∑uv∈ef(uv)(mod2) for each v∈v‎, ‎where z2={0,1} is the additive group of order 2‎. ‎for i∈{0,1}‎, ‎let‎ ‎ef(i)=|f−1(i)| and vf(i)=|(f+)−1(i)|‎. ‎a labeling f is called edge-friendly if‎ ‎|ef(1)−ef(0)|≤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.