Discussiones Mathematicae Graph Theory 32(3) (2012) 535-543
doi: 10.7151/dmgt.1623

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On Super (a,d)-edge Antimagic Total Labeling of Certain Families of Graphs

P. Roushini Leely Pushpam

Department of Mathematics
D.B. Jain College, Chennai - 600097
Tamil Nadu, India

A. Saibulla

Department of Mathematics
B.S. Abdur Rahman University, Chennai - 600048
Tamil Nadu, India


A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f : V(G) ∪E(G) → {1, 2, ..., p+q} such that the edge weights L(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2,..., p} and the edge labels are {p+1, p+2, ...,p+q}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.

Keywords: edge weight, magic labeling, antimagic labeling, ladder, fan graph, prism and web graph

2010 Mathematics Subject Classification: 05C78, 05C76.


[1]M. Bača and C. Barrientos, Graceful and edge antimagic labelings, Ars Combin. 96 (2010) 505--513.
[2]M. Bača, Y. Lin, M. Miller and R. Simanjuntak, New construction of magic and antimagic graph labeling, Util. Math. 60 (2001) 229--239.
[3]H. Enomoto, A.S. Llodo, T. Nakamigawa and G. Ringel, Super edge magic graphs, SUT J. Math. 34 (1998) 105--109.
[4]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, doi: 10.1016/S0012-365X(00)00314-9.
[5]J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 17 (2010) #DS6.
[6]F. Harrary, Graph Theory ( Addison-Wesley, 1994).
[7]N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press, Boston, San Diego, New York, London, 1990).
[8]S.M. Hegde and Sudhakar Shetty, On magic graphs, Australas. J. Combin. 27 (2003) 277--284.
[9]A. Kotzig and A. Rosa, Magic valuation of finite graphs, Canad. Math. Bull. 13 (1970) 451--461, doi: 10.4153/CMB-1970-084-1.
[10]R. Simanjuntak, F. Bertault and M. Miller, Two new (a, d)-antimagic graph labelings, Proc. Eleventh Australian Workshop Combin. Algor., Hunrer Valley, Australia (2000) 179--189.
[11]K.A. Sugeng and M. Miller, Relationship between adjacency matrices and super (a, d)-edge antimagic total labelings of graphs, J. Combin. Math. Combin. Comput. 55 (2005) 71--82.
[12]K.A. Sugeng, M. Miller and M. Bača, Super edge antimagic total labelings, Util. Math. 71 (2006) 131--141.

Received 15 March 2011
Revised 2 August 2011
Accepted 23 September 2011