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ANTIMAGIC LABELING OF THE UNION OF SUBDIVIDED STARS

Year 2016, Volume: 6 Issue: 2, 244 - 250, 01.12.2016

Abstract

Enomoto et al. 1998 de ned the concept of a super a; 0 -edge-antimagic total labeling and proposed the conjecture that every tree is a super a; 0 -edge-antimagic total labeling. In support of this conjecture, the present paper deals with di erent results on antimagicness of subdivided stars and their unions.

References

  • Kotzig,A. and Rosa,A., (1970), Magic valuations of finite graphs, Canad. Math. Bull., 13, pp. 451-461.
  • Kotzig,A. and Rosa,A., (1972), Magic valuation of complete graphs, Centre de Recherches Mathema- tiques, Universite de Montreal, CRM-175.
  • Salman,A.N.M., Ngurah,A.A.G. and Izzati,N., (2010), On Super Edge-Magic Total Labeling of a
  • Subdivision of a Star Sn, Utilitas Mathematica, 81, pp. 275-284. Baskoro,E.T. and Ngurah,A.A.G., (2003), On super edge-magic total labelings, Bull. Inst. Combin. Appil., 37, pp. 82-87.
  • Ngurah,A.A.G., Simanjuntak,R. and Baskoro,E.T., (2007), On (super) edge-magic total labeling of subdivision of K1,3, SUT J. Math. 43, pp. 127-136.
  • Enomoto,H., Llado,A.S., Nakamigawa,T. and Ringle,G., (1980), Super edge-magic graphs, SUT J. Math. 34, pp. 105-109.
  • Gallian,J.A., (2010), A dynamic survey of graph labeling, J. Combin. January.
  • Sugeng,K.A., Miller,M. , Slamin and Baˇca,M., (2005), (a, d)-edge-antimagic total labelings of cater- pillars, Lecture Notes Comput. Sci., 3330, pp. 169–180.
  • Baˇca,M., Lin,Y. and Muntaner-Batle,F.A., (2010), Edge-antimagic labeling of forests, Utilitas Math., , pp. 31-40.
  • Baˇca,M. and Barrientos,C., (2010), Graceful and edge-antimagic labeling, Ars Combin, 96, pp. 505
  • Baˇca,M., Kov´aˇr,P., Semaniˇcov´a-Feˇnovˇc´ıkov´a,A. and Shafig,M.K., (2010), On super (a, 1)-edge- antimagic total labeling of regular graphs, Discrete Math., 310, pp. 1408-1412.
  • Baˇca,M., Lin,Y., Miller,M. and Youssef,M.Z., (2007), Edge-antimagic graphs, Discrete Math., 307, pp. 1232-1244.
  • Baˇca,M., Lin,Y., Miller,M. and Simanjuntak,R., (2001), New constructions of magic and antimagic graph labelings, Utilitas Math., 60, pp. 229-239.
  • Baˇca,M., Lin,Y. and Muntaner-Batle,F.A., (2007), Super edge-antimagic labelings of the path-like trees, Utilitas Math., 73, pp. 117-128.
  • Baˇca,M., Semaniˇcov´a-Feˇnovˇc´ıkov´a,A. and Shafig,M.K., (2011), A method to generate large classes of edge-antimagic trees, Utilitas Math., 86, pp. 33-43.
  • Hussain,M., Baskoro,E.T. and Slamin, (2009), On super edge-magic total labeling of banana trees, Utilitas Math., 79, pp. 243-251.
  • Javaid,M., Hussain,M., Ali,K. and Shaker,H., Super edge-magic total labeling on subdivision of trees, Utilitas Math. to appear. Javaid,M., Hussain,M., Ali,K. and Dar,K.H., (2011), Super edge-magic total labeling on w − trees, Utilitas Math., 86, pp. 183-191.
  • Figueroa-Centeno,R.M., Ichishima,R. and Muntaner-Batle,F.A., (2001), The place of super edge- magic labeling among other classes of labeling, Discrete Math., 231, pp. 153-168.
  • Figueroa-Centeno,R.M., Ichishima,R. and Muntaner-Batle,F.A., (2002), On super edge-magic graph, Ars Combin., 64, pp. 81-95.
  • Simanjuntak,R., Bertault,F. and Miller,M., (2000), Two new (a, d)-antimagic graph labelings, Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms, pp. 179-189.
  • Lee,S.M. and Shah,Q.X.,(2002), All trees with at most 17 vertices are super edge-magic, 16th MCCCC
  • Conference, Carbondale, University Southern Illinois. Fukuchi,Y., (2002), A recursive theorem for super edge-magic labeling of trees, SUT J. Math., 36, pp. 285.
  • Yong,J.L., (2001), A proof of three-path trees P (m, n, t) being edge-magic, College Mathematica, 17:2, pp. 41-44.
  • Yong,J.L., (2004), A proof of three-path trees P (m, n, t) being edge-magic (II), College Mathematica, :3, pp. 51-53.
Year 2016, Volume: 6 Issue: 2, 244 - 250, 01.12.2016

Abstract

References

  • Kotzig,A. and Rosa,A., (1970), Magic valuations of finite graphs, Canad. Math. Bull., 13, pp. 451-461.
  • Kotzig,A. and Rosa,A., (1972), Magic valuation of complete graphs, Centre de Recherches Mathema- tiques, Universite de Montreal, CRM-175.
  • Salman,A.N.M., Ngurah,A.A.G. and Izzati,N., (2010), On Super Edge-Magic Total Labeling of a
  • Subdivision of a Star Sn, Utilitas Mathematica, 81, pp. 275-284. Baskoro,E.T. and Ngurah,A.A.G., (2003), On super edge-magic total labelings, Bull. Inst. Combin. Appil., 37, pp. 82-87.
  • Ngurah,A.A.G., Simanjuntak,R. and Baskoro,E.T., (2007), On (super) edge-magic total labeling of subdivision of K1,3, SUT J. Math. 43, pp. 127-136.
  • Enomoto,H., Llado,A.S., Nakamigawa,T. and Ringle,G., (1980), Super edge-magic graphs, SUT J. Math. 34, pp. 105-109.
  • Gallian,J.A., (2010), A dynamic survey of graph labeling, J. Combin. January.
  • Sugeng,K.A., Miller,M. , Slamin and Baˇca,M., (2005), (a, d)-edge-antimagic total labelings of cater- pillars, Lecture Notes Comput. Sci., 3330, pp. 169–180.
  • Baˇca,M., Lin,Y. and Muntaner-Batle,F.A., (2010), Edge-antimagic labeling of forests, Utilitas Math., , pp. 31-40.
  • Baˇca,M. and Barrientos,C., (2010), Graceful and edge-antimagic labeling, Ars Combin, 96, pp. 505
  • Baˇca,M., Kov´aˇr,P., Semaniˇcov´a-Feˇnovˇc´ıkov´a,A. and Shafig,M.K., (2010), On super (a, 1)-edge- antimagic total labeling of regular graphs, Discrete Math., 310, pp. 1408-1412.
  • Baˇca,M., Lin,Y., Miller,M. and Youssef,M.Z., (2007), Edge-antimagic graphs, Discrete Math., 307, pp. 1232-1244.
  • Baˇca,M., Lin,Y., Miller,M. and Simanjuntak,R., (2001), New constructions of magic and antimagic graph labelings, Utilitas Math., 60, pp. 229-239.
  • Baˇca,M., Lin,Y. and Muntaner-Batle,F.A., (2007), Super edge-antimagic labelings of the path-like trees, Utilitas Math., 73, pp. 117-128.
  • Baˇca,M., Semaniˇcov´a-Feˇnovˇc´ıkov´a,A. and Shafig,M.K., (2011), A method to generate large classes of edge-antimagic trees, Utilitas Math., 86, pp. 33-43.
  • Hussain,M., Baskoro,E.T. and Slamin, (2009), On super edge-magic total labeling of banana trees, Utilitas Math., 79, pp. 243-251.
  • Javaid,M., Hussain,M., Ali,K. and Shaker,H., Super edge-magic total labeling on subdivision of trees, Utilitas Math. to appear. Javaid,M., Hussain,M., Ali,K. and Dar,K.H., (2011), Super edge-magic total labeling on w − trees, Utilitas Math., 86, pp. 183-191.
  • Figueroa-Centeno,R.M., Ichishima,R. and Muntaner-Batle,F.A., (2001), The place of super edge- magic labeling among other classes of labeling, Discrete Math., 231, pp. 153-168.
  • Figueroa-Centeno,R.M., Ichishima,R. and Muntaner-Batle,F.A., (2002), On super edge-magic graph, Ars Combin., 64, pp. 81-95.
  • Simanjuntak,R., Bertault,F. and Miller,M., (2000), Two new (a, d)-antimagic graph labelings, Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms, pp. 179-189.
  • Lee,S.M. and Shah,Q.X.,(2002), All trees with at most 17 vertices are super edge-magic, 16th MCCCC
  • Conference, Carbondale, University Southern Illinois. Fukuchi,Y., (2002), A recursive theorem for super edge-magic labeling of trees, SUT J. Math., 36, pp. 285.
  • Yong,J.L., (2001), A proof of three-path trees P (m, n, t) being edge-magic, College Mathematica, 17:2, pp. 41-44.
  • Yong,J.L., (2004), A proof of three-path trees P (m, n, t) being edge-magic (II), College Mathematica, :3, pp. 51-53.
There are 24 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

A. Abdul Raheem This is me

B. Abdul Qudair Baig This is me

Publication Date December 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 2

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