On Super Edge-Antimagic Total Labeling of Toeplitz Graphs

Bača, Martin; Bashir, Yasir; Nadeem, Muhammad Faisal; Shabbir, Ayesha

doi:10.1007/978-3-0348-0859-0_1

Cited by 5 publications

(8 citation statements)

References 10 publications

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“…The dual labeling notion has been presented by [10]. The lemma follows from the duality principal, which is review by [11].…”

Section: Description 11 a (P D)-edge-antimagic Vertex ((P D)-eav) mentioning

confidence: 99%

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Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Mathew¹

2015

DJ JEAM

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In the existing method the authors assume that there admits in every tree a labeling of edgemagic total. The existing author proposed the speculations that every tree is a super (b, d)-graph of edge-antimagic total.In this proposed paper, we frame the subdivided star super (b, d)-edge-antimagic total labeling , n 5 , n 6 ..., n q ) for d ∈ {0, 1, 2}, where q ≥ 5, n s , 5 ≤ s≤ q and n ≥ 3 is odd.

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“…The dual labeling notion has been presented by [10]. The lemma follows from the duality principal, which is review by [11].…”

Section: Description 11 a (P D)-edge-antimagic Vertex ((P D)-eav) mentioning

confidence: 99%

“…• [10] proved the existence of a super (b, o)-labeling of EAT on the star of subdivided classes denoted by S n m for m = 1, 2, where…”

Section: Description 21mentioning

confidence: 99%

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Mathew¹

2015

DJ JEAM

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“…These labelings are the generalization of the edge-magic and super edge-magic labelings that were introduced by Kotzig and Rosa [2] and Enomoto et al [3], respectively. For further information about (super) edgemagic labelings, one can see [4][5][6][7][8]. Gutiérrez and Lladó [1] proved that certain classes of connected graphs are -(super)magic, such as the star 1, and the complete bipartite graphs , are 1,ℎ -supermagic for some ℎ.…”

Section: Introductionmentioning

confidence: 99%

Tree-Antimagicness of Disconnected Graphs

Bača

Kimáková

Semaničová-Feňovčíková

et al. 2015

Mathematical Problems in Engineering

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A simple graphGadmits anH-covering if every edge inE(G)belongs to a subgraph ofGisomorphic toH. The graphGis said to be (a,d)-H-antimagic if there exists a bijection from the vertex setV(G)and the edge setE(G)onto the set of integers1, 2, …,VG+E(G)such that, for all subgraphsH′ofGisomorphic toH, the sum of labels of all vertices and edges belonging toH′constitute the arithmetic progression with the initial termaand the common differenced.Gis said to be a super (a,d)-H-antimagic if the smallest possible labels appear on the vertices. In this paper, we study super tree-antimagic total labelings of disjoint union of graphs.

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“…Some constructions of super (a, d)-edgeantimagic total labelings for the disjoint union of stars and the disjoint union of s-Crowns have been shown by Dafik et al (2008) and Bača et al (2009) respectively, and super (a, d)-edgeantimagic total labelings for disjoint union of caterpillars have been described by Bača et al (2008). Dafik et al (2013) also found some families of well-defined Graph which admits super (a, d)-edge-antimagic total labelings, namely Triangular Book and Diamond Ladder.…”

Section: Introductionmentioning

confidence: 99%

“…The concept of super edge-magic labeling, firstly defined by Enomoto et al (1998) gave motivations to other researchers to investigate the different forms of antimagic graphs. For example, Bača et al (2008), Bača et al (2001), and Dafik et al (2008) investigated the existence of the super (a, d)-edge-antimagic total graph.…”

Section: Introductionmentioning

confidence: 99%

Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph

Sumarno

Dafik²,

Santoso³

2015

J. I. Dasar

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Abstract. Let G be a simple graph of order p and size q.G r a p hG is called an (a, d)-edge-antimagic total if there exist a bijection f : V (G) ∪ E(G) →{1, 2,...,p+ q} such that the edge-weights, w(uv)= f (u)+f (v)+f (uv); u, v ∈ V (G),uv ∈ E(G),formanarithmeticsequencewithfirstterma and common difference d.S u c hag r a p hG is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge antimagic total properties of connected of Ferris Wheel FWm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs admit a super (a, d)-edge antimagic total labeling for d =0, 1, 2.I tc a nb ec o n c l u d e dt h a tt h er e s u l to ft h i sr e s e a r c hh a sc o v e red all feasible d.

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On Super Edge-Antimagic Total Labeling of Toeplitz Graphs

Cited by 5 publications

References 10 publications

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Tree-Antimagicness of Disconnected Graphs

Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph

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