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On The Balanced Windmill Graphs

机译:关于平衡的风车图

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摘要

Let G be a graph with vertex set V(G) and edge set E(G), and let A ={0,1}. A labeling f: V(G) → A induces an edge partial labeling f~* : E(G) → A defined by Οf~*(xy) = f(x), if and only if f(x)=f(y) for each edge xy ∈ E(G). For i ∈ A, let v_f(i) = card {v ∈ V(G) : f(v) = i} and e_(f*)(i) = card{e ∈ E(G) : f~*(e) = i). A labeling f of a graph G is said to be friendly if | v_f(0)- v_f(l) | ≤ 1. If, | _f(0) -e_f(l) I < 1 then G is said to be balanced. In this paper we prove several families of regular windmill and general windmill graphs are balanced.
机译:令G为具有顶点集V(G)和边集E(G)的图,令A = {0,1}。标记f:V(G)→A诱导边缘部分标记f〜*:E(G)→A由of〜*(xy)= f(x)定义,当且仅当f(x)= f( y)对于每个边xy∈E(G)。对于i∈A,令v_f(i)=卡{v∈V(G):f(v)= i}和e_(f *)(i)=卡{e∈E(G):f〜*( e)= i)。如果| |,则表示图G的标记f是友好的。 v_f(0)-v_f(l)| ≤1。 _f(0)-e_f(l)如果I <1,则称G是平衡的。在本文中,我们证明了常规风车的几个族和普通风车图是平衡的。

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