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