4 research outputs found

    Cycle-magic graphs

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    AbstractA simple graph G=(V,E) admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. Then the graph G is C-magic if there exists a total labelling f:V∪E→{1,2,…,|V|+|E|} such that, for every subgraph H′=(V′,E′) of G isomorphic to C, ∑v∈V′f(v)+∑e∈E′f(e) is constant. When f(V)={1,…,|V|}, then G is said to be C-supermagic.We study the cyclic-magic and cyclic-supermagic behavior of several classes of connected graphs. We give several families of Cr-magic graphs for each r⩾3. The results rely on a technique of partitioning sets of integers with special properties

    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, ∑v∈V(H)f(v)+∑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

    Magic and antimagic labeling of graphs

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    "A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."Doctor of Philosoph

    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 λ:V∪E→{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)=λ(x)+∑y:xy∈Eλ(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 λ:V∪E→{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)=λ(x)+λ(y)+λ(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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