一类新的魔术染色(英文)

A New Type of Magical Coloring

借鉴于Kotzig和Rosa在1970年定义的边魔术全标号,我们给具有p个顶点和q条边的图G定义了一个新的染色标号,叫作k-魔术染色f,其中f是一一映射V(G)∪E(G)→{1,2,…,p+q},使得任何边uv∈E(G)满足f(u)+f(v)=k+f(uv),并得到超级k-魔术染色的概念.我们得到了一些具有k-魔术染色或超级k-魔术染色图的性质以及构造这些图的方法.最后,我们猜测所有的树具有一个超级k-魔术染色.

Motivated from the edge-magic total labelling defined by Kotzig and Rosa（1970）, we define a nearly k-magic coloring f of a graph G with p vertices and q edges that is a bijection from V（G） U E（G） to {1, 2,...,p ＋ q} such that ｜f（u） ＋ f（v） - f（uv）｜≤ k whenever uv E E（G）. We have some results on a k-magic coloring f of G which is a nearly k-magic coloring of G and keeps f（u） ＋ f（v） = k ＋ f（uv） for uv ∈ E（G）. Furthermore, we study some graphs with a supper k-magic coloring f that is k-magic coloring and f（u） ≤ p for all u ∈ V（G）. We find some ways to construct some graphs having k-magic coloring or supper k-magic coloring, and show some properties about such graphs. At the end of this paper, we conjecture that any tree has a supper k-magic coloring.