Super edge magic graceful graphs
Super edge magic graceful graphs
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超边缘魔法曼妙图
DOI：
10.1016/j.ins.2014.07.027
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Balakrishnan
中科院分区：
文献类型：
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作者：
G. Marimuthu;M. Balakrishnan
具有p个顶点和q条边的（p，q）图G是边幻优美的，如果存在一个双射f：V（G）<$E（G）→{1，2，.，p+ q}使得|f（u）+ f（v）-f（uv）|= k，G的任意边uv的常数。若f（V（G））={1，2，.，p}，则称G是超边幻优美的.本文给出了超边幻优美图的一些性质。利用这些性质，我们证明了某些图类是超边幻优美图。然后，我们展示了超边魔优美标号和其他研究得很好的标号类之间的关系。特别地，我们证明了对任意uv∈ E（G）满足f（uv）> f（u）+ f（v）或对任意uv∈ E（G）满足f（uv）< f（u）+ f（v）的超边幻优美图是序列的、协调的、超边幻的和非优美的.
A (p, q) graph G with p vertices and q edges is edge magic graceful if there exists a bijection f: V (G)∪ E (G)→{1, 2,…, p+ q} such that| f (u)+ f (v)-f (uv)|= k, a constant for any edge uv of G. G is said to be super edge magic graceful if f (V (G))={1, 2,…, p}. In this paper we present some properties of super edge magic graceful graphs. Using these properties, we prove some classes of graphs are super edge magic graceful. Then we exhibit the relationship between super edge magic graceful labeling and other well studied classes of labelings. In particular, we prove that every super edge magic graceful graph with either f (uv)> f (u)+ f (v) for all uv∈ E (G) or f (uv)< f (u)+ f (v) for all uv∈ E (G) is sequential, harmonious, super edge magic and not graceful.