8 research outputs found
Supermagic graphs with many different degrees
Let G = (V, E) be a graph with n vertices and e edges. A supermagic labeling of G is a bijection f from the set of edges E to a set of consecutive integers {a, a + 1,..., a + e - 1} such that for every vertex v is an element of V the sum of labels of all adjacent edges equals the same constant k. This k is called a magic constant of f, and G is a supermagic graph.
The existence of supermagic labeling for certain classes of graphs has been the scope of many papers. For a comprehensive overview see Gallian's Dynamic survey of graph labeling in the Electronic Journal of Combinatorics. So far, regular or almost regular graphs have been studied. This is natural, since the same magic constant has to be achieved both at vertices of high degree as well as at vertices of low degree, while the labels are distinct consecutive integers.Web of Science4141050104
Swap-Robust and Almost Supermagic Complete Graphs for Dynamical Distributed Storage
To prevent service time bottlenecks in distributed storage systems, the
access balancing problem has been studied by designing almost supermagic edge
labelings of certain graphs to balance the access requests to different
servers. In this paper, we introduce the concept of robustness of edge
labelings under limited-magnitude swaps, which is important for studying the
dynamical access balancing problem with respect to changes in data popularity.
We provide upper and lower bounds on the robustness ratio for complete graphs
with vertices, and construct -almost supermagic labelings that are
asymptotically optimal in terms of the robustness ratio.Comment: 27 pages, no figur
Vertex Magic Group Edge Labelings
A project submitted to the faculty of the graduate school of the University of Minnesota in partial fulfillment of the requirements for the degree of Master of Science. May 2017. Major: Mathematics and Statistics. Advisor: Dalibor Froncek. 1 computer file (PDF); vi, 46 pages, appendix A, Ill. (some col.)A vertex-magic group edge labeling of a graph G(V;E) with |E| = n is an injection from
E to an abelian group ᴦ of order n such that the sum of labels of all incident edges of
every vertex x ϵ V is equal to the same element µ ϵ ᴦ. We completely characterize all
Cartesian products Cn□Cm that admit a vertex-magic group edge labeling by Z2nm, as
well as provide labelings by a few other finite abelian groups
Magic and antimagic labeling of graphs
"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
Algebraic Combinatorics of Magic Squares
We describe how to construct and enumerate Magic squares, Franklin squares,
Magic cubes, and Magic graphs as lattice points inside polyhedral cones using
techniques from Algebraic Combinatorics. The main tools of our methods are the
Hilbert Poincare series to enumerate lattice points and the Hilbert bases to
generate lattice points. We define polytopes of magic labelings of graphs and
digraphs, and give a description of the faces of the Birkhoff polytope as
polytopes of magic labelings of digraphs.Comment: Ph.D. Thesi
An extensive English language bibliography on graph theory and its applications
Bibliography on graph theory and its application
Chemical Youth
This open access book explores how young people engage with chemical substances in their everyday lives. It builds upon and supplements a large body of literature on young people’s use of drugs and alcohol to highlight the subjectivities and socialities that chemical use enables across diverse socio-cultural settings, illustrating how young people seek to avoid harm, while harnessing the beneficial effects of chemical use. The book is based on multi-sited anthropological research in Southeast Asia, Europe and the US, and presents insights from collaborative and contrasting analysis. Hardon brings new perspectives to debates across drug policy studies, pharmaceutical cultures and regulation, science and technology studies, and youth and precarity in post-industrial societies
Chemical Youth
This open access book explores how young people engage with chemical substances in their everyday lives. It builds upon and supplements a large body of literature on young people’s use of drugs and alcohol to highlight the subjectivities and socialities that chemical use enables across diverse socio-cultural settings, illustrating how young people seek to avoid harm, while harnessing the beneficial effects of chemical use. The book is based on multi-sited anthropological research in Southeast Asia, Europe and the US, and presents insights from collaborative and contrasting analysis. Hardon brings new perspectives to debates across drug policy studies, pharmaceutical cultures and regulation, science and technology studies, and youth and precarity in post-industrial societies