On Super Edge-Antimagic Total Labeling of Generalized Extended W-Trees

Javaid, Muhammad

doi:10.26708/ijmsc.2014.1.4.03

Cited by 7 publications

(5 citation statements)

References 9 publications

(6 reference statements)

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“…Such labelings were called irregular assignments and the irregularity strength s(G) of a graph G is known as the minimum k for which G has irregular assignments using labels atmost k. Some results on irregularity strength s(G) of a graph G can be found in [1,3,6,7,8,12,13,14,15,16,17,18,19,20,21,22,23]. Let φ be a vertex labeling of a graph G. Then we define the edge weight of xy ∈ E(G) to be w(xy) = φ(x) + φ(y).…”

Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Further results on edge irregularity strength of graphs

Imran

Aslam

Zafar

et al. 2017

IJC

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A vertex k-labelling φ : V (G) −→ {1, 2, . . . , k} is called irregular k-labeling of the graph G if for every two different edges e and f , there is w φ (e) = w φ (f ); where the weight of an edge is given by e = xy ∈ E(G) is w φ (xy) = φ(x) + φ(y). The minimum k for which the graph G has an edge irregular k-labelling is called edge irregularity strength of G, denoted by es(G). In the paper, we determine the exact value of the edge irregularity strength of caterpillars, n-star graphs, (n, t)-kite graphs, cycle chains and friendship graphs.

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Section: Introduction and Preliminary Resultsmentioning

confidence: 99%

Further results on edge irregularity strength of graphs

Imran

Aslam

Zafar

et al. 2017

IJC

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“…. , p 􏼈 􏼉 such that w θ (x) ≠ w θ (y) for all x ≠ y ∈ V of a graph G. Te least value p is the irregularity strength, and the highest label of graph G. Tis variable has attracted much attention of researchers [2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

On Valuation of Edge Irregularity Strength of Certain Graphical Families

Zhang

Tariq

Rehman

et al. 2022

Journal of Mathematics

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This article comprises of exact valuation of a graph parameter, known as the edge irregularity strength EIS , symbolized as eis G , of various graphical families such as middle graph of path graph, middle graph of cycle graph, snake graph (string 2), paramedian ladder, and complete m -partite graphs. If δ : V ⟶ 1,2 , … , p is a function defined on vertices of a graph that helps to determine different weights for every pair of edges, the least value of p is the target. Thus, addition operation for allocated to vertices of an edge, i.e., δ v i + δ v j , i ≠ j = 1,2 , … , n , defines the weight w δ v i v j of corresponding edge for every v i v j ∈ E . If two different edges e i and e j in graph G carry weights in different manner, i.e., w δ e i ≠ w δ e i for i ≠ j . Then the edge irregular p -labeling is defined after a vertex p -labeling of G . After establishing various novel results and making some conclusions, an open problem is mentioned in the end.

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“…For trees having maximum of seventeen vertices, in [8], this conjecture has been verified. For instance, the S − (a, 0) − EAMT labeling on a class of trees termed as w-trees can be observed in [9]. Similarly, S − (a, 0) − EAMT labeling on various classes consisting of subdivisions of trees can be seen in [10,11].…”

Section: Introductionmentioning

confidence: 99%

Enumeration of the Edge Weights of Symmetrically Designed Graphs

Javaid

Afzal

Bonyah³

2021

Journal of Mathematics

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The idea of super a , 0 -edge-antimagic labeling of graphs had been introduced by Enomoto et al. in the late nineties. This article addresses super a , 0 -edge-antimagic labeling of a biparametric family of pancyclic graphs. We also present the aforesaid labeling on the disjoint union of graphs comprising upon copies of C 4 and different trees. Several problems shall also be addressed in this article.

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On Super Edge-Antimagic Total Labeling of Generalized Extended W-Trees

Abstract: This paper deals with the construction of generalized extended w-trees denoted by GEwt(n, m, r, k) and the existence of a super (a, d)-edge-antimagic total labeling on them for d ∈ {0, 1, 2}.

Cited by 7 publications

References 9 publications

Further results on edge irregularity strength of graphs

Further results on edge irregularity strength of graphs

On Valuation of Edge Irregularity Strength of Certain Graphical Families

Enumeration of the Edge Weights of Symmetrically Designed Graphs

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