【摘要】 n个顶点ε条边的图G,它的最小平衡值为d,本文的主要结论是:当n3-1≤d≤n-2时,ε≤(n-d-1)(d+1),等号成立当且仅当G同构于K1,1,,1,d+1.我们将证明在给定的d中满足|dG(u)-dG(v)|≥d的条件下,文章中所确定的ε是最好的上界.更多还原

【Abstract】 If for a graph G of order n and size ε the minimum imbalance of an edge of G equals d,then our mian result states that ε ≤(n-d -1)(d + 1),if n-3-1 ≤ d ≤ n-2,with equality if and only if G is isomorphic to K1,1,,1,d+1.we also prove best possible upper bounds on the number of edges uv of a graph G such that |d G(u)-d G(v)|≥d for some given d.更多还原