On edge-balance index sets of the complete graphs
Yurong Ji, Yuge Zheng · 2010
Let G be a simple graph with vertex setV(G)and edge setE(G), and letZ2= {0, 1}, For a given binary edge labelingf:E(G)→Z2, the edge labeling f induces a partial vertex labelingf*:V(G)→Z2such thatf*:V(G) = 1(0)iff the number of 1-edges (0-edges) is strictly greater than the number of 0-edges (l-edges) incident to v, otherwisef*(v)is undefined. ForiϵZ2, let v(i) = card{vϵV(G):f*(v) = i}. and e(i) = card{eϵE(G):f(e) = i}, The edge-balance index sets of a graphG,EBI(G), is defined as{|v(0)-v(1)|:the edge labeling f satisfies|e(0)-e(1)|≤1}. In this paper, we completely determine the edge-balance index sets of the complete graphs with constructive proof.