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

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

Abstract

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.

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