The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

On Super Edge-Antimagic Total Labeling Of Subdivided Stars

Muhammad Javaid

Discussiones Mathematicae Graph Theory (2014)

  • Volume: 34, Issue: 4, page 691-706
  • ISSN: 2083-5892

Abstract

top
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.

How to cite

top

Muhammad Javaid. "On Super Edge-Antimagic Total Labeling Of Subdivided Stars." Discussiones Mathematicae Graph Theory 34.4 (2014): 691-706. <http://eudml.org/doc/269825>.

@article{MuhammadJavaid2014,
abstract = {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.},
author = {Muhammad Javaid},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {super (a; d)-EAT labeling; subdivision of star.; super -EAT labeling; subdivision of star},
language = {eng},
number = {4},
pages = {691-706},
title = {On Super Edge-Antimagic Total Labeling Of Subdivided Stars},
url = {http://eudml.org/doc/269825},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Muhammad Javaid
TI - On Super Edge-Antimagic Total Labeling Of Subdivided Stars
JO - Discussiones Mathematicae Graph Theory
PY - 2014
VL - 34
IS - 4
SP - 691
EP - 706
AB - 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.
LA - eng
KW - super (a; d)-EAT labeling; subdivision of star.; super -EAT labeling; subdivision of star
UR - http://eudml.org/doc/269825
ER -

References

top
  1. [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 Zbl1120.05075
  2. [2] M. Bača, Y. Lin, M. Miller and R. Simanjuntak, New constructions of magic and antimagic graph labelings, Util. Math. 60 (2001) 229-239. Zbl1011.05056
  3. [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. Zbl1140.05049
  4. [4] M. Bača and M. Miller, Super Edge-Antimagic Graphs (Brown Walker Press, Boca Raton, Florida USA, 2008). 
  5. [5] H. Enomoto, A.S. Lladó, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998) 105-109. Zbl0918.05090
  6. [6] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. (2011) #DS6. Zbl0953.05067
  7. [7] M. Hussain, E.T. Baskoro and Slamin, On super edge-magic total labeling of banana trees, Util. Math. 79 (2009) 243-251. Zbl1215.05150
  8. [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. Zbl1267.05230
  9. [9] M. Javaid and A.A. Bhatti, On super (a, d)-edge antimagic total labeling of subdivided stars, Ars Combin. 105 (2012) 503-512. Zbl1274.05421
  10. [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. Zbl1264.05119
  11. [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. Zbl1264.05120
  12. [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. Zbl1300.05275
  13. [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 Zbl0213.26203
  14. [14] A. Kotzig and A. Rosa, Magic Valuation of Complete Graphs (Centre de Recherches Mathematiques, Uni. de Montreal, 1972). 
  15. [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. [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. [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. [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. Zbl1175.05116
  19. [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. Zbl1214.05153
  20. [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 Zbl1117.05096
  21. [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. [22] D.B. West, An Introduction to Graph Theory (Prentice Hall, 1996). Zbl0845.05001

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.