On Connection Between \(\alpha\)-Labelings and Edge-Antimagic Labelings of Disconnected Graphs

Abstract

A labeling of a graph is any map that carries some set of graph elements to numbers (usually to the positive integers). An \((a, d)\)-edge-antimagic total labeling on a graph with \(p\) vertices and \(q\) edges is defined as a one-to-one map taking the vertices and edges onto the integers \(1,2,…,p+q\) with the property that the sums of the labels on the edges and the labels of their endpoints form an arithmetic sequence starting from \(a\) and having a common difference \(d\). Such a labeling is called super if the smallest possible labels appear on the vertices.

We use the connection between \(a\)-labelings and edge-antimagic labelings for determining a super \((a,d)\)-edge-antimagic total labelings of disconnected graphs.