New Methods for Magic Total Labelings of Graphs

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New Methods for Magic Total Labelings of Graphs

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Singgih, Inne

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2015-05

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Abstract

A \textit{vertex magic total (VMT) labeling} of a graph $G=(V,E)$ is a bijection from the set of vertices and edges to the set of numbers defined by $\lambda:V\cup E\rightarrow\{1,2,\dots,|V|+|E|\}$ so that for every $x \in V$ and some integer $k$, $w(x)=\lambda(x)+\sum_{y:xy\in E}\lambda(xy)=k$. An \textit{edge magic total (EMT) labeling} is a bijection from the set of vertices and edges to the set of numbers defined by $\lambda:V\cup E\rightarrow\{1,2,\dots,|V|+|E|\}$ so that for every $xy \in E$ and some integer $k$, $w(xy)=\lambda(x)+\lambda(y)+\lambda(xy)=k$. Numerous results on labelings of many families of graphs have been published. In this thesis, we include methods that expand known VMT/EMT labelings into VMT/EMT labelings of some new families of graphs, such as unions of cycles, unions of paths, cycles with chords, tadpole graphs, braid graphs, triangular belts, wheels, fans, friendships, and more.

Keywords

Edge Magic Total Labeling

Kotzig array

Vertex Magic Total Labeling

Description

University of Minnesota M.S. thesis. May 2015. Major: Mathematics. Advisors: Dalibor Froncek, Sylwia Cichacz-Przenioslo. 1 computer file (PDF); ix, 117 pages.

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Singgih, Inne. (2015). New Methods for Magic Total Labelings of Graphs. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/191213.

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