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

Authors:
K. A. Sugeng;M. Miller; Slamin;M. Bača
Affiliations:
School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia;School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria, Australia;FKIP, Universitas Jember, Indonesia;Department of Appl. Mathematics, Technical University, Košice, Slovak Republic
Venue:
IJCCGGT'03 Proceedings of the 2003 Indonesia-Japan joint conference on Combinatorial Geometry and Graph Theory
Year:
2003

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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)-edge-antimagic total properties of stars Sn and caterpillar Sn1,n2,...,nr.