Vertex magic total labelings of 2-regular graphs

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• 作者：Sylwia Cichacz^a ; ^b ; Dalibor Froncek^a ; ^{dfroncek@d.umn.edu" class="auth_mail" title="E-mail the corresponding author} ; Inne Singgih^a ; ^c
• 关键词：Magic-type labelings ; Vertex magic total labelings
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：6 January 2017
• 年：2017
• 卷：340
• 期：1
• 页码：3117-3124
• 全文大小：908 K

文摘

A vertex magic total (VMT) labeling   of a graph a70821aca" title="Click to view the MathML source">G=(V,E)$G=(V,E)$ is a bijection from the set of vertices and edges to the set of integers defined by bd" title="Click to view the MathML source">λ:V∪E→{1,2,…,|V|+|E|}$\lambda :V\cup E\to \{1,2,\dots ,|V|+|E\left|\right\}$ so that for every ae2c4" title="Click to view the MathML source">x∈V$x\in V$, bdf6359187b0898dbd0122e4" title="Click to view the MathML source">w(x)=λ(x)+∑_xy∈Eλ(xy)=k$w\left(x\right)=\lambda \left(x\right)+{\sum }_{xy\in E}\lambda \left(xy\right)=k$, for some integer e58c21af1" title="Click to view the MathML source">k$k$. A VMT labeling is said to be a super   VMT labeling if the vertices are labeled with the smallest possible integers, bdae6d53782aafd73326bdb158d" title="Click to view the MathML source">1,2,…,|V|$1,2,\dots ,\left|V\right|$. In this paper we introduce a new method to expand some known VMT labelings of 2-regular graphs.