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Antimagic Labeling of Cubic Graphs
Journal of Graph Theory, 2014Summary: An antimagic labeling of a graph \(G\) is a one-to-one correspondence between \(E(G)\) and \(\{1,2,\ldots,|E|\}\) such that the sum of the labels assigned to edges incident to distinct vertices are different. If \(G\) has an antimagic labeling, then we say \(G\) is antimagic. This article proves that cubic graphs are antimagic.
Xuding Zhu, Yu-Chang Liang
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Graph antimagic labeling: A survey
Discrete Mathematics, Algorithms and Applications, 2023An antimagic labeling of a simple graph [Formula: see text] is a bijection [Formula: see text] such that [Formula: see text] for any two vertices [Formula: see text] in [Formula: see text]. We survey the results about antimagic labelings and other labelings motivated by antimagic labelings of graphs, and present some conjectures and open questions.
Jingxiang Jin, Zhuojie Tu
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Antimagic Labelings of Join Graphs
Mathematics in Computer Science, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Martin Baca +3 more
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Local Super Antimagic Total Labeling for Vertex Coloring of Graphs
Symmetry, 2020 Let G=(V,E) be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from V∪E to {1,2,…,|V|+|E|} such that if for each uv∈E(G) then w(u)≠w ...
Kristiana Wijaya
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Face Antimagic Labeling of Jahangir Graph
Mathematics in Computer Science, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muhammad Kamran Siddiqui +2 more
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Distance Antimagic Labelings of Graphs
2017Let \(G=(V,E)\) be a graph of order n. Let \(f: V(G)\rightarrow \{1,2,\dots ,n\}\) be a bijection. For any vertex \(v \in V,\) the neighbor sum \(\sum \limits _{u\in N(v)}f(u)\) is called the weight of the vertex v and is denoted by w(v). If \(w(x) \ne w(y)\) for any two distinct vertices x and y, then f is called a distance antimagic labeling. A graph
Nainarraj Kamatchi +4 more
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Antimagic labelling of vertex weighted graphs
Journal of Graph Theory, 2011AbstractSuppose G is a graph, k is a non‐negative integer. We say G is k‐antimagic if there is an injection f: E→{1, 2, …, |E| + k} such that for any two distinct vertices u and v, . We say G is weighted‐k‐antimagic if for any vertex weight function w: V→ℕ, there is an injection f: E→{1, 2, …, |E| + k} such that for any two distinct vertices u and v, .
Tsai-Lien Wong, Xuding Zhu
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Graceful and Antimagic Labelings
2019This chapter explores the relationship between antimagic labeling and alpha labelings and also the well-known graceful labelings. Much of this chapter looks at interesting labelings and structures on trees, including edge antimagic trees, alpha trees, and disjoint union of caterpillars.
Martin Bača +3 more
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On Antimagic Labeling of Odd Regular Graphs
2012An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, ⋯ , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling.
Tao-Ming Wang, Guang-Hui Zhang
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Innovative Perspectives on Antimagic Labeling in Graphs
International Journal of Mathematics and Computer ScienceThe graph G represents an undirected, simple, finite graph. G's total labeling is a bijection between its vertex and edge sets and the set {1, 2,..., p+q}, where p and q describe the cardinality of G's vertex and edge sets, respectively. In this paper, we explore the concept of Super Vertex Perfectly Total Antimagic (SVPTAT) labeling in the context of
Sundar, S. Bala +4 more
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