Super Face Antimagic Labelings of Union of Antiprisms

Bača, Martin; Numan, Muhammad; Siddiqui, Muhammad Kamran

doi:10.1007/s11786-013-0152-y

Cited by 16 publications

(17 citation statements)

References 7 publications

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“…The existence of d-antimagic labeling for special classes of plane graphs with 3-sided internal faces is given in [1]. The super d-antimagic labelings of type (1, 1, 1) for antiprisms and for d ∈ {0, 1, 2, 3, 4, 5, 6} are described in [6], and for disjoint union of m copies of antiprism mA n , m ≥ 2, n ≥ 4 and for d ∈ {1, 2, 3, 5, 6} are given in [18]. For disjoint union of prisms and for d ∈ {0, 1, 2, 3, 4, 5} are given in [3].…”

Section: Introductionmentioning

confidence: 99%

On face antimagic labeling of strong face plane graphs

Ahmed¹,

Babujee²

2017

ams

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Let G = (V (G), E(G), F (G)) be a simple, finite, connected, plane graph with the vertex set V (G), the edge set E(G) and the face set F (G). A labeling of type (1, 1, 1) assigns labels from the set {1, 2,. .. , |V (G)| + |E(G)| + |F (G)|} to the vertices, edges and faces of a plane graph G, such that each vertex, edge and face receives exactly one label and each number is used exactly once as a label. Moreover, the labeling is called super if the vertices are lebaled with the smallest numbers. The weight of a face under the labeling of type (1, 1, 1) is sum of labels of the face itself and vertices and edges surrounding that face. A labeling of a plane graph is called d-antimagic if for every positive integer s the set of weights of all s-sided faces is W s ={a s , a s + d,. .. , a s + (ν s − 1)d} for some integers a s and d ≥ 0, where ν s is the number of the s-sided faces. In this paper we study (super) d-antimagic labeling of type (1, 1, 1) for some strong face plane graphs.

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Section: Introductionmentioning

confidence: 99%

On face antimagic labeling of strong face plane graphs

Ahmed¹,

Babujee²

2017

ams

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“…The super d-antimagic labelings of type (1, 1, 1) for antiprisms are described in [4] and for disjoint union of prisms are given in [1]. The existence of super dantimagic labeling of type (1, 1, 1) for the plane graphs containing a special Hamilton path is examined in [5] and for disconnected plane graphs are investigated in [11].…”

Section: Introductionmentioning

confidence: 99%

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

2016

Self Cite

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The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. Classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons. A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. In this paper we examine the existence of entire labeling, where face-weights of all 6-sided faces of disjoint union of toroidal fullerenes form an arithmetic progression with common difference d ∈ {1, 2, 3}.

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“…Bača determined magic labeling on different graphs in [2,3,4,6,8,9]. Siddiqui [15] determined the existence of super d-antimagic labeling for a Jahangir graph for certain different d. Bača [7,11,12,13] gave magic labelings of type (1,1,1 ) and type ( 1,1,0) for certain classes of convex polytopes. A general survey of graph labelings is given in [18] .…”

Section: Introductionmentioning

confidence: 99%

Super d-anti-magic labeling of subdivided $kC_{5}$

Hussain¹,

Tabraiz²

2015

Turk J Math

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|} to the vertices, edges, and faces of a planar graph G in such a way that each vertex, edge, and face receives exactly one label and each number is used exactly once as a label and the weight of each face under the mapping is the same. Super d -antimagic labeling of type (1, 1, 1) on snake kC5 , subdivided kC5 as well as ismorphic copies of kC5 for string (1, 1, ..., 1) and string (2, 2, ..., 2) is discussed in this paper.

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Super Face Antimagic Labelings of Union of Antiprisms

Cited by 16 publications

References 7 publications

On face antimagic labeling of strong face plane graphs

On face antimagic labeling of strong face plane graphs

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

Super d-anti-magic labeling of subdivided $kC_{5}$

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