2,267 research outputs found

    Vertex (A,d)-antimagic Total Labeling on Circulant Graph Cn(1,2,3)

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    H-E-Super Magic Decomposition of Graphs

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    An H-magic labeling in an H-decomposable graph G is a bijection f:V(G) U E(G) --> {1,2, … ,p+q} such that for every copy H in the decomposition, βˆ‘v∈V(H)f(v)+βˆ‘e∈E(H)f(e)\sum\limits_{v\in V(H)} f(v)+\sum\limits_{e\in E(H)} f(e) is constant. The function f is said to be H-E-super magic if f(E(G)) = {1,2, … ,q}. In this paper, we study some basic properties of m-factor-E-super magic labelingand we provide a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable. For this purpose, we use Petersen\u27s theorem and magic squares

    New Methods for Magic Total Labelings of Graphs

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    University of Minnesota M.S. thesis. May 2015. Major: Mathematics. Advisors: Dalibor Froncek, Sylwia Cichacz-Przenioslo. 1 computer file (PDF); ix, 117 pages.A \textit{vertex magic total (VMT) labeling} of a graph G=(V,E)G=(V,E) is a bijection from the set of vertices and edges to the set of numbers defined by Ξ»:VβˆͺEβ†’{1,2,…,∣V∣+∣E∣}\lambda:V\cup E\rightarrow\{1,2,\dots,|V|+|E|\} so that for every x∈Vx \in V and some integer kk, w(x)=Ξ»(x)+βˆ‘y:xy∈EΞ»(xy)=kw(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 Ξ»:VβˆͺEβ†’{1,2,…,∣V∣+∣E∣}\lambda:V\cup E\rightarrow\{1,2,\dots,|V|+|E|\} so that for every xy∈Exy \in E and some integer kk, w(xy)=Ξ»(x)+Ξ»(y)+Ξ»(xy)=kw(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
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