54 research outputs found
Regular graphs of odd degree are antimagic
An antimagic labeling of a graph with edges is a bijection from
to such that for all vertices and , the sum of
labels on edges incident to differs from that for edges incident to .
Hartsfield and Ringel conjectured that every connected graph other than the
single edge has an antimagic labeling. We prove this conjecture for
regular graphs of odd degree.Comment: 5 page
An Inductive Approach to Strongly Antimagic Labelings of Graphs
An antimagic labeling for a graph with edges is a bijection so that holds for any pair
of distinct vertices , where .
A strongly antimagic labeling is an antimagic labeling with an additional
condition: For any , if , then . A graph is strongly antimagic if it admits a strongly antimagic
labeling. We present inductive properties of strongly antimagic labelings of
graphs. This approach leads to simplified proofs that spiders and double
spiders are strongly antimagic, previously shown by Shang [Spiders are
antimagic, Ars Combinatoria, 118 (2015), 367--372] and Huang [Antimagic
labeling on spiders, Master's Thesis, Department of Mathematics, National
Taiwan University, 2015], and by Chang, Chin, Li and Pan [The strongly
antimagic labelings of double spiders, Indian J. Discrete Math. 6 (2020),
43--68], respectively. We fix a subtle error in [The strongly antimagic
labelings of double spiders, Indian J. Discrete Math. 6 (2020), 43--68].
Further, we prove certain level-wise regular trees, cycle spiders and cycle
double spiders are all strongly antimagic
Group-antimagic Labelings of Multi-cyclic Graphs
Let be a non-trivial abelian group. A connected simple graph is -\textbf{antimagic} if there exists an edge labeling such that the induced vertex labeling , defined by , is a one-to-one map. The \textit{integer-antimagic spectrum} of a graph is the set IAM. In this paper, we analyze the integer-antimagic spectra for various classes of multi-cyclic graphs
SOME RESULTS OF LABELING ON BROOM GRAPH
A Broom Graph Bn,d is a graph of n vertices, which have a path P with d vertices and (n-d) pendant vertices, all of these being adjacent to either the origin u or the terminus v of the path P. Here we consider various labeling on Broom graph such as Cordial labeling, Antimagic labeling and b-coloring.
 
A SURVEY OF DISTANCE MAGIC GRAPHS
In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . . , n}, such that for every vertex x Σ l(y) = k,y∈NG(x)
where NG(x) is the set of vertices of G adjacent to x. If the graph G has a distance magic labeling we say that G is a distance magic graph.
In Chapter 1, we explore the background of distance magic graphs by introducing examples of magic squares, magic graphs, and distance magic graphs.
In Chapter 2, we begin by examining some basic results on distance magic graphs. We next look at results on different graph structures including regular graphs, multipartite graphs, graph products, join graphs, and splitting graphs. We conclude with other perspectives on distance magic graphs including embedding theorems, the matrix representation of distance magic graphs, lifted magic rectangles, and distance magic constants.
In Chapter 3, we study graph labelings that retain the same labels as distance magic labelings, but alter the definition in some other way. These labelings include balanced distance magic labelings, closed distance magic labelings, D-distance magic labelings, and distance antimagic labelings.
In Chapter 4, we examine results on neighborhood magic labelings, group distance magic labelings, and group distance antimagic labelings. These graph labelings change the label set, but are otherwise similar to distance magic graphs.
In Chapter 5, we examine some applications of distance magic and distance antimagic labeling to the fair scheduling of tournaments.
In Chapter 6, we conclude with some open problems
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