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ANTIMAGIC LABELING OF THE UNION OF SUBDIVIDED STARS

Yıl 2016, Cilt: 6 Sayı: 2, 244 - 250, 01.12.2016

Öz

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.

Kaynakça

  • 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.
Yıl 2016, Cilt: 6 Sayı: 2, 244 - 250, 01.12.2016

Öz

Kaynakça

  • 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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

A. Abdul Raheem Bu kişi benim

B. Abdul Qudair Baig Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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