(a, d)-Edge-antimagic total labelings of caterpillars

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 with initial term a and common difference d. An (a, d)-edge-antimagic total labeling g is called super (a, d)-edge-antimagic total if g(V(G)) = (1,2,. ..,|V(G)|}. We study super (a,d)-6idge-antimagic total properties of stars Sn and caterpillar Sn1, n2,...n 1. © Springer-Verlag Berlin Heidelberg 2005.