Super (a, d)-edge antimagic total labeling of some classes of graphs

Abstract

A graph G(V, E) is (a, d)-edge antimagic total if there exists a bijection f: V (G) ∪ E(G) → {1, 2,..., |V (G)| + |E(G)|} such that the edge weights Λ(uv) = f (u) + f (uv) + f (v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if f (V (G)) = {1, 2,..., |V (G)|}. In this paper, we have obtained a relation between a super (a, 0)-edge antimagic total labeling and a super (a, 2) edge antimagic total labeling of any graph. Also we study the super (a, d)-edge antimagic total labeling of fan graphs and two special classes of star graphs namely bi-star and extended bi-star.