Scholarly article on topic 'On super edge-antimagic total labeling of subdivided stars'

On super edge-antimagic total labeling of subdivided stars Academic research paper on "Mathematics"

0
0
Share paper
Academic journal
Discuss. Math. Graph Theory
OECD Field of science
Keywords
{""}

Academic research paper on topic "On super edge-antimagic total labeling of subdivided stars"

Discussiones Mathematicae Graph Theory 34 (2014) 691-706 doi: 10.7151/dmgt. 1764

ON SUPER EDGE-ANTIMAGIC TOTAL LABELING OF SUBDIVIDED STARS1

Muhammad Javaid

Department of Mathematics National University of Computer and Emerging Sciences, Lahore Campus, Pakistan

e-mail: mjavaidmath@gmail.com javaidmath@gmail.com

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 support 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.

Keywords: super (a, d)-EAT labeling, subdivision of star. 2010 Mathematics Subject Classification: 05C78.

References

[1] M. Baca, 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. Baca, Y. Lin, M. Miller and R. Simanjuntak, New constructions of 'magic and antimagic graph labelings, Util. Math. 60 (2001) 229-239.

[3] M. Baca, Y. Lin and F.A. Muntaner-Batle, Super edge-antimagic labelings of the path-like trees, Util. Math. 73 (2007) 117-128.

[4] M. Baca and M. Miller, Super Edge-Antimagic Graphs (Brown Walker Press, Boca Raton, Florida USA, 2008).

xThe research contents of this paper are partially supported by the Higher Education Commission (HEC) of Pakistan.

[5] H. Enomoto, A.S. Llado, 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 K13, 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. Baca, (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 labelings , in: Proc. 11th Australian Workshop on Combin. Algor. 11 (2000) 179-189.

22] D.B. West, An Introduction to Graph Theory (Prentice Hall, 1996).

Received 11 June 2012 Revised 2 October 2013 Accepted 2 October 2013

Copyright of Discussiones Mathematicae: Graph Theory is the property of Discussiones Mathematicae Graph Theory and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.