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2014 | 34 | 4 | 691-706
Tytuł artykułu

On Super Edge-Antimagic Total Labeling Of Subdivided Stars

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In 1980, Enomoto et al. proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In this paper, we give a partial sup- port for the correctness of this conjecture by formulating some super (a, d)- edge-antimagic total labelings on a subclass of subdivided stars denoted by T(n, n + 1, 2n + 1, 4n + 2, n5, n6, . . . , nr) for different values of the edge- antimagic labeling parameter d, where n ≥ 3 is odd, nm = 2m−4(4n+1)+1, r ≥ 5 and 5 ≤ m ≤ r.
Słowa kluczowe
Wydawca
Rocznik
Tom
34
Numer
4
Strony
691-706
Opis fizyczny
Daty
wydano
2014-11-01
otrzymano
2012-06-11
poprawiono
2013-10-02
zaakceptowano
2013-10-02
online
2014-11-15
Twórcy
  • Department of Mathematics National University of Computer and Emerging Sciences, Lahore Campus, Pakistan, mjavaidmath@gmail.com
Bibliografia
  • [1] M. Bača, Y. Lin, M. Miller and M.Z. Youssef, Edge-antimagic graphs, Discrete Math. 307 (2007) 1232-1244. doi:10.1016/j.disc.2005.10.038
  • [2] M. Bača, Y. Lin, M. Miller and R. Simanjuntak, New constructions of magic and antimagic graph labelings, Util. Math. 60 (2001) 229-239.
  • [3] M. Bača, Y. Lin and F.A. Muntaner-Batle, Super edge-antimagic labelings of the path-like trees, Util. Math. 73 (2007) 117-128.
  • [4] M. Bača and M. Miller, Super Edge-Antimagic Graphs (Brown Walker Press, Boca Raton, Florida USA, 2008).
  • [5] H. Enomoto, A.S. Lladó, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998) 105-109.
  • [6] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2011) #DS6.
  • [7] M. Hussain, E.T. Baskoro and Slamin, On super edge-magic total labeling of banana trees, Util. Math. 79 (2009) 243-251.
  • [8] M. Javaid, M. Hussain, K. Ali and H. Shaker, On super edge-magic total labeling on subdivision of trees, Util. Math. 89 (2012) 169-177.
  • [9] M. Javaid and A.A. Bhatti, On super (a, d)-edge antimagic total labeling of subdivided stars, Ars Combin. 105 (2012) 503-512.
  • [10] M. Javaid, A.A. Bhatti and M. Hussain, On (a, d)-edge-antimagic total labeling of extended w-trees, Util. Math. 87 (2012) 293-303.
  • [11] M. Javaid, M. Hussain, K. Ali and K.H. Dar, Super edge-magic total labeling on w-trees, Util. Math. 86 (2011) 183-191.
  • [12] M. Javaid, A.A. Bhatti, M. Hussain and K. Ali, Super edge-magic total labeling on forest of extended w-trees, Util. Math. 91 (2013) 155-162.
  • [13] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13 (1970) 451-461. doi:10.4153/CMB-1970-084-1
  • [14] A. Kotzig and A. Rosa, Magic Valuation of Complete Graphs (Centre de Recherches Mathematiques, Uni. de Montreal, 1972).
  • [15] S.M. Lee and Q.X. Shah, All trees with at most 17 vertices are super edge-magic, in: 16th MCCCC Conference, Carbondale SIU (2002).
  • [16] Y.-J. Lu, A proof of three-path trees P(m, n, t) being edge-magic, College Mathe- matica 17(2) (2001) 41-44.
  • [17] Y.-J. Lu, A proof of three-path trees P(m, n, t) being edge-magic (II), College Math- ematica 20(3) (2004) 51-53.
  • [18] A.A.G. Ngurah, R. Simanjuntak and E.T. Baskoro, On (super) edge-magic total labeling of subdivision of K1,3, SUT J. Math. 43 (2007) 127-136.
  • [19] A.N.M. Salman, A.A.G. Ngurah and N. Izzati, On super edge-magic total labeling of a subdivision of a star Sn, Util. Math. 81 (2010) 275-284.
  • [20] K.A. Sugeng, M. Miller, Slamin and M. Baˇca, (a, d)-edge-antimagic total labelings of caterpillars, Lect. Notes Comput. Sci. 3330 (2005) 169-180. doi:10.1007/978-3-540-30540-8 19
  • [21] R. Simanjuntak, F. Bertault and M. Miller, Two new (a, d)-antimagic graph label- ings, in: Proc. 11th Australian Workshop on Combin. Algor. 11 (2000) 179-189.
  • [22] D.B. West, An Introduction to Graph Theory (Prentice Hall, 1996).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1764
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