Pelabelan total tak-ajaib sisi pada multistar

Abstract

Graph theory contains several topics, one of which will be discussed in this study is graph labeling. In the topic of labeling, the graph used is a limited, simple, and undirected graph. In this study, the type of labeling used is total labeling. The multistar graph used in this study is a combination of star graphs whose center vertex are not connected to each other. This research uses literature research method which is divided into two parts, that is the basic calculation to determine the boundary of the first term 𝑎𝑎 and the difference 𝑑𝑑 from the (𝑎𝑎,𝑑𝑑) edge antimagic total labeling on the 𝑚𝑚𝑆𝑆𝑛𝑛 multistar graph. The second part is to apply (𝑎𝑎,𝑑𝑑) edge antimagic total labeling to the multistar graph 𝑚𝑚𝑆𝑆𝑛𝑛. In multistar 𝑚𝑚𝑆𝑆𝑛𝑛 can be labeled by (𝑎𝑎,𝑑𝑑) edge antimagic total labeling by 􁉀3𝑚𝑚2𝑛𝑛2+5𝑚𝑚2𝑛𝑛+4𝑚𝑚𝑚 2𝑚𝑚𝑚 ,1􁉁 and 􁉀2𝑚𝑚2𝑛𝑛2+5𝑚𝑚2𝑛𝑛+5𝑚𝑚𝑚 2𝑚𝑚𝑚 ,2􁉁 for center label smallest value, with 𝑚𝑚≥1 and 𝑛𝑛≥2. Otherwise, for center label largest value can be done by 􁉀7𝑚𝑚2𝑛𝑛2+𝑚𝑚2𝑛𝑛+4𝑚𝑚𝑚 2𝑚𝑚𝑚 ,1􁉁and 􁉀6𝑚𝑚2𝑛𝑛2+𝑚𝑚2𝑛𝑛+5𝑚𝑚𝑚 2𝑚𝑚𝑚 ,2􁉁 with 𝑚𝑚≥1 and 𝑛𝑛≥2.