Super Edge Antimagic Total Labeling On Disjoint Union Of Cycle With Chord
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Abstract
A graph with order and size is called -edge antimagic total ( -EAT) if there exist integers , and a bijection such that , where . An -EAT labeling of graph is super if . In this paper we describe how to construct a super -EAT labeling on some classes of disjoint union from non isomorphic graphs, namely disjoint union of cycle with cycle with chord .
Keywords: -edge-antimagictotallabeling,super -edgeantimagictotalla- belling, cycle with chord,
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References
[1] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13, (1970), 451–461.
[2] Dafik, M. Miller, J. Ryan and M. Baˇca, On super (a, d)-edge antimagic total labeling of disconnected graphs, Discrete Math., 309 (2009), 4909–4915.
[3] G. Ringel and A.S. Llad´o, Another tree conjecture, Bull. Inst. Combin. Appl. 18, (1996), 83–85.
[4] H. Enomoto, A.S. Llad´o, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998), 105–109.
[5] I.W. Sudarsana, D. Ismaimuza, E.T. Baskoro and H. Assiyatun, On super (a, d)- edge antimagic total labeling of disconnected graphs, JCMCC 55 (2005), 149–158.
[6] J. A. Gallian, A Dynamic Survey of Graph Labelling, Electronic Journal Combinatorics, # DS6, (2016).
[7] J. Ivanˇco and I. Luˇckaniˇcov´a, On edge-magic disconnected graphs, SUT Journal of Math. 38 (2002), 175–184.
[8] K.A. Sugeng, M. Miller, Slamin and M. Baˇca, (a, d)-edge-antimagic total labelings of caterpillars, Lecture Notes in Computer Science 3330 (2005), 169–180.
[9] M. Baˇca, Y. Lin, M. Miller and R. Simanjuntak, New constructions of magic and antimagic graph labelings, Utilitas Math. 60 (2001), 229–239.
[10] M. Baˇca and M. Miller, Super Edge Antimagic Graphs, Brown Walker Press, Boca Raton, (2008).
[11] M. Baˇca, Dafik, M. Miller and J. Ryan, On super (a, d)-edge antimagic total
[12] labeling of caterpillars, J. Combin. Math. Combin. Comput., 65 (2008), 61–70.
[13] N. Hartsfield and G. Ringel,Pearls in Graph Theory, Academic Press, San Diego, (1994).
[14] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, The place of super edge-magic labelings among other classes of labelings, Discrete Math. 231 (2001), 153–168.
[15] R. Simanjuntak, F. Bertault and M. Miller, Two new (a, d)-antimagic graph labelings, Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms (2000), 179–189.
[16] W. D. Wallis, E. T. Baskoro, M. Miller and Slamin , Edge-magic total labelings, Austral. J. Combin. 22 (2000), 177–190.
[2] Dafik, M. Miller, J. Ryan and M. Baˇca, On super (a, d)-edge antimagic total labeling of disconnected graphs, Discrete Math., 309 (2009), 4909–4915.
[3] G. Ringel and A.S. Llad´o, Another tree conjecture, Bull. Inst. Combin. Appl. 18, (1996), 83–85.
[4] H. Enomoto, A.S. Llad´o, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998), 105–109.
[5] I.W. Sudarsana, D. Ismaimuza, E.T. Baskoro and H. Assiyatun, On super (a, d)- edge antimagic total labeling of disconnected graphs, JCMCC 55 (2005), 149–158.
[6] J. A. Gallian, A Dynamic Survey of Graph Labelling, Electronic Journal Combinatorics, # DS6, (2016).
[7] J. Ivanˇco and I. Luˇckaniˇcov´a, On edge-magic disconnected graphs, SUT Journal of Math. 38 (2002), 175–184.
[8] K.A. Sugeng, M. Miller, Slamin and M. Baˇca, (a, d)-edge-antimagic total labelings of caterpillars, Lecture Notes in Computer Science 3330 (2005), 169–180.
[9] M. Baˇca, Y. Lin, M. Miller and R. Simanjuntak, New constructions of magic and antimagic graph labelings, Utilitas Math. 60 (2001), 229–239.
[10] M. Baˇca and M. Miller, Super Edge Antimagic Graphs, Brown Walker Press, Boca Raton, (2008).
[11] M. Baˇca, Dafik, M. Miller and J. Ryan, On super (a, d)-edge antimagic total
[12] labeling of caterpillars, J. Combin. Math. Combin. Comput., 65 (2008), 61–70.
[13] N. Hartsfield and G. Ringel,Pearls in Graph Theory, Academic Press, San Diego, (1994).
[14] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, The place of super edge-magic labelings among other classes of labelings, Discrete Math. 231 (2001), 153–168.
[15] R. Simanjuntak, F. Bertault and M. Miller, Two new (a, d)-antimagic graph labelings, Proc. of Eleventh Australasian Workshop on Combinatorial Algorithms (2000), 179–189.
[16] W. D. Wallis, E. T. Baskoro, M. Miller and Slamin , Edge-magic total labelings, Austral. J. Combin. 22 (2000), 177–190.
