On (a, d)-edge-antimagic total iabelings of extended w-trees

Abstract

Let G = (V,E) be a graph with υ = |V(G)| vertices and e = |-E(G)| edges. An (a, d)-edge-antimagic total labeling is a bijection γ from V(G) ∪ E(G) to the set of consecutive integers {1,2,..., υ + e} such that the edge-weights {w(xy): w(xy) = γ(x) + γ(y) + γ(xy),xy ∈ E(G)} form an arithmetic progression with the initial term a and common difference d. Additionally, if γ(V(G)) = {1,2,...,υ} then the labeling γ is super (a, d)-edge-antimagic total. In this paper we construct super (a, d)-edge-antimagic total labeling for extended w-trees as well as super (a, d)-edge-antimagic total labeling for disjoint union of isomorphic and non-isomorphic copies of extended w-trees.