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Edge-antimagic graphs

Abstract:

For a graph G = (V, E), a bijection g from V (G) ∪ E (G) into { 1, 2, ...,| V (G) | + | E (G) | } is called (a, d)-edge-antimagic total labeling of G if the edge-weights w (xy) = g (x) + g (y) + g (xy), xy ∈ E (G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if g (V (G)) = { 1, 2, ..., | V (G) | }. We study super (a, d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs. © 2007 Elsevier B.V. All rights reserved.