Labelings of type (1,1,1) for toroidal fullerenes

Bača, Martin; Numan, Muhammad; Shabbir, Ayesha

doi:10.3906/mat-1207-13

Cited by 10 publications

(11 citation statements)

References 11 publications

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“…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]. The super d-antimagic labelings of type (1, 1, 1) for toroidal fullerenes are described in [12].…”

Section: Introductionmentioning

confidence: 99%

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

2016

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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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Section: Introductionmentioning

confidence: 99%

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

2016

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“…Motivated by the paper [15] we deal with the super d-antimagic labelings of type (1, 1, 1) for the toroidal grid and we describe those labelings for several values of d.…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Face antimagic labelings of toroidal and Klein bottle grid graphs

Butt

Numan

Ali

et al. 2020

AKCE International Journal of Graphs and Combinatorics

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In this paper we deal with the problem of labeling the vertices, edges and faces of a toroidal T m n and Klein bottle K m n grid graphs with mn 4-sided faces by the consecutive integers from 1 up to |V (T m n)| + |E(T m n)| + |F(T m n)| and |V (K m n)| + |E(K m n)| + |F(K m n)| in such a way that the label of a 4-sided face and the labels of the vertices and edges surrounding that face all together add up to a weight of that face. These face-weights then form an arithmetic progression with common difference d. The paper examines the existence of such labelings for several differences d.

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“…The existence of super d-antimagic labeling of type (1, 1, 1) for the plane graphs containing a special Hamilton path is examined in [10] and super d-antimagic labelings of type (1, 1, 1) for disconnected plane graphs are investigated in [16]. The super d-antimagic labelings of type (1, 1, 1) for friendship graphs F n , n ≥ 2 and several other families of planar graphs are given in [9] and for toroidal polyhex H n m are given in [17]. The super d-antimagic labelings of type (1, 1, 0) for friendship graphs F n , n ≥ 2, for d ∈ {1, 3, 5, 7, 9, 11, 13} and for d ∈ {0, 2, 4, 6, 8, 10}, n is odd are given in [8].…”

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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Labelings of type (1,1,1) for toroidal fullerenes

Cited by 10 publications

References 11 publications

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

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

Face antimagic labelings of toroidal and Klein bottle grid graphs

On face antimagic labeling of strong face plane graphs

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