Strong edge antimagic total labeling on multistar

Abstract

Strong edge antimagic total labelling of a simple graph G(V,E) is graph labelling which the vertex labels are consecutive integers from 1 to |V| such that, the weight of edges, i.e. the total label of the vertices incident to the edge, will form an ascending arithmetic sequence. This article discusses this kind of vertex labelling on multistar graphs. A multistar graph is an unconnected combination of star graphs. The study is a literature study with a mathematical proof. The results of the study is that multistar graphs have a strong edge antimagic total labelling. Furthermore, the labelling can be done on an unconnected combination of m star graphs and the difference of the weight of the edges are 1 and 2 with initial term \(a=\frac{5mn+3m+4}{2}\) and \(a=\frac{4mn+3m+5}{2}\), respectively.