Topic
Magic graph
About: Magic graph is a research topic. Over the lifetime, 47 publications have been published within this topic receiving 2623 citations.
Papers
Journal Article•
TL;DR: In this survey I have collected everything I could find on graph labelings techniques that have appeared in journals that are not widely available.
Abstract: A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.
2,831 citations
TL;DR: A survey of distance magic graphs can be found in this paper, where the authors present a survey of existing results along with their recent results, open problems and conjectures, as well as some recent conjectures.
Abstract: Let G = (V;E) be a graph of order n. A bijection f : V r {1, 2,...,n} is called a distance magic labeling of G if there exists a positive integer k such that S f(u) = k for all v e V, where N(v) is the open neighborhood of v. The constant k is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. In this paper we present a survey of existing results on distance magic graphs along with our recent results,open problems and conjectures. DOI : http://dx.doi.org/10.22342/jims.0.0.15.11-26
93 citations
Journal Article•
TL;DR: All orders n for which a 4-regular distance magic graph exists is classified and it is shown that there exists a distancemagic graph with k = 2 for every integer t ≥ 6.
Abstract: Let G =( V,E) be a graph on n vertices. A bijection f : V →{ 1, 2,...,n} is called a distance magic labeling of G if there exists an integer k such thatu∈N(v) f (u )= k for all v ∈ V , where N(v) is the set of all vertices adjacent to v. The constant k is the magic constant of f and any graph which admits a distance magic labeling is a distance magic graph .I n this paper we solve some of the problems posted in a recent survey paper on distance magic graph labelings by Arumugam et al. We classify all orders n for which a 4-regular distance magic graph exists and by this we also show that there exists a distance magic graph with k =2 t for every integer t ≥ 6.
15 citations
TL;DR: It is shown that if 2e>=10n^2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three, and the upper and lower bounds of any vertex degree in terms of n and e are obtained.
14 citations
1 Jan 2013
TL;DR: In this article, the authors show some Γ distance magic labelings for Cm Cn, where Γ ∼= Zmn, and deal with group distance labeling of the pth power of a cycle Cn.
Abstract: Let G = (V,E) be a graph and Γ an abelian group, both of order n. A group distance magic labeling of G is a bijection : V → Γ for which there exists μ ∈ Γ such that ∑x∈N(v) (x) = μ for all v ∈ V, where N(v) is the neighborhood of v. Froncek [Australas. J. Combin. 55 (2013), 167–174] showed that the cartesian product Cm Cn, m,n ≥ 3 is a Zmn-distance magic graph if and only if mn is even. In this paper we show some Γdistance magic labelings for Cm Cn where Γ ∼= Zmn. Moreover we will deal with group distance labeling of the pth power of a cycle Cn.
12 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 3 |
| 2020 | 3 |
| 2019 | 2 |
| 2018 | 2 |
| 2017 | 3 |
| 2016 | 1 |