ANTIMAGIC LABELING OF THE UNION OF SUBDIVIDED STARS
Year 2016,
Volume: 6 Issue: 2, 244 - 250, 01.12.2016
A. Abdul Raheem
B. Abdul Qudair Baig
Abstract
Enomoto et al. 1998 dened 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 dierent 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
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- 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
A. Abdul Raheem
B. Abdul Qudair Baig
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.