Super (a, 3)-edge-antimagic total labelings for union of two stars

Abstract

An (a, d)-edge-antimagic total labeling of a graph G = (V, E) with p vertices and q edges is a bijection f: V ∪ E → {1,2,3,...,p + q} such that all the edge-weights ω(uv) = f(u) + f(v) + f(uv); uv ∈ E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called a super (a, d)-edge-antimagic total labeling ((a, d)-SEAMT labeling) if f(V(G)) = {1,2,3,...,p}. In this paper we investigate the existence of (a, 3)-SEAMT labelings for union of two stars.