In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.
📌 3 Key Takeaways
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Objective & Hypothesis:A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H′ of G isomorphic to H, wtf (H′) = ∑v∈V (H′)f(v) + ∑e∈E(H′)f(e), form an arithmetic progression a, a+d, . . . , a+(t−1)d, where a is the first term, d is the common difference and t is the number of subgraphs in the H-covering.
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Key Findings & Data:If f(V ) = {1, 2, . . . , |V |}, then f is called super (a, d)-H-antimagic labeling.
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Conclusion & Impact:In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
A simple graph G = (V, E) admitting an H-covering is said to be (a, d)-H-antimagic if there exists a bijection f : V ∪ E → {1, 2, . . . , |V | + |E|} such that, for all subgraphs H′ of G isomorphic to H, wtf (H′) = ∑v∈V (H′)f(v) + ∑e∈E(H′)f(e), form an arithmetic progression a, a+d, . . . , a+(t−1)d, where a is the first term, d is the common difference and t is the number of subgraphs in the H-covering. Then f is called an (a, d)-H-antimagic labeling. If f(V ) = {1, 2, . . . , |V |}, then f is called super (a, d)-H-antimagic labeling. In this paper we investigate the existence of super (a,d)-star-antimagic labelings of a particular class of banana trees and construct a star-antimagic graph.
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Cite This Article
SELVAGOPAL, P. N., JEYANTHİ, P., MUTHURAJA, T., SEMONİCOVA-FENOVCİKOVA, A. (2022). Super(a,d)-star-antimagic graphs. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 3, 700–710. https://ajindex.com/articles/529729
M. Bača, Z. Kimáková, A. Semaničová-Feňovčíková and M.A. Umar,Tree-antimagicness of disconnected graphs, Math. Probl. Eng.2015, Article ID: 504251,1–4, 2015. [2]M. Bača, M. Miller, J. Ryan and A. Semaničová-Feňovčíková,OnH-antimagicnessof disconnected graphs, Bull. Aust. Math. Soc.94, 201–207, 2016. [3]A. Gutiérrez and A. Lladó,Magic coverings, J. Combin. Math. Combin. Comput.55,43–56, 2005. [4]N. Inayah, A.N.M. Salman and R. Simanjuntak,On(a, d)-H-antimagic coverings ofgraphs, J. Combin. Math. Combin. Comput.71, 273–281, 2009. [5]N. Inayah, R. Simanjuntak, A.N.M. Salman and K.I.A. Syuhada,On(a, d)-H-antimagic total labelings for shackles of a connected graphH, Australas. J. Combin.57, 127–138, 2013. [6]P. Jeyanthi and P. Selvagopal,Supermagic coverings of some simple graphs, Int. J.Math. Combin.1, 33–48, 2011. [7]T.K. Maryati, A.N.M. Salman, E.T. Baskoro, J. Ryan and M. Miller,OnH-supermagic labelings for certain shackles and amalgamations of a connected graph,Utilitas Math.83, 333–342, 2010. [8]A. Semaničová-Feňovčíková, M. Bača, M. Lascsáková, M. Miller and J. Ryan,Wheelsare cycle-antimagic, Electron. Notes Discrete Math.48, 11–18, 2015.