27 research outputs found
Cycle-magic graphs
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
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
Magic coverings and the Kronecker product
In this paper we study a relationship existing among (super) magic coverings and the
well known Kronecker product of matrices. We also introduce the concept of Zn–property
for digraphs in order to study this relation mentioned before. The results obtained in this
paper can also be applied to construct S–magic partitions.Preprin
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
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
Total Rainbow Connection Number Of Shackle Product Of Antiprism Graph (〖AP〗_3)
Function if is said to be k total rainbows in , for each pair of vertex there is a path called with each edge and each vertex on the path will have a different color. The total connection number is denoted by trc defined as the minimum number of colors needed to make graph to be total rainbow connected. Total rainbow connection numbers can also be applied to graphs that are the result of operations. The denoted shackle graph is a graph resulting from the denoted graph where t is number of copies of G. This research discusses rainbow connection numbers rc and total rainbow connection trc(G) using the shackle operation, where is the antiprism graph . Based on this research, rainbow connection numbers rc shack , and total rainbow connection trc shack for .Fungsi jika c : G → {1,2,. . . , k} dikatakan k total pelangi pada G, untuk setiap pasang titik terdapat lintasan disebut x-y dengan setiap sisi dan setiap titik pada lintasan akan memiliki warna berbeda. Bilangan terhubung total pelangi dilambangkan dengan trc(G), didefinisikan sebagai jumlah minimum warna yang diperlukan untuk membuat graf G menjadi terhubung-total pelangi. Bilangan terhubung total pelangi juga dapat diterapkan pada graf yang merupakan hasil operasi. Graf shackle yang dilambangkan (G1,G2,…,Gt) adalah graf yang dihasilkan dari graf G yang dilambangkan (G,t) dengan t adalah jumlah salinan dari Penelitian ini membahas mengenai bilangan terhubung pelangi rc dan bilangan terhubung total pelangi trc(G)menggunakan operasi shackle, dimana G adalah graf Antiprisma (AP3)Berdasarkan penelitian ini, diperoleh bilangan terhubung pelangi rc(shack AP3,t )= t+2, dan total pelangi trc(shack AP3,t)=2t+3 untuk t ≥2
H-E-Super Magic Decomposition of Graphs
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, 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