Antimagic Total Dekomposisi Graf Helm dan untuk Pengembangan Ciphertext

Abstract

A graph $G(V,E)$ has a $H$-Covering if every edge in $E$ belongs to a subgraph of $G$ isomorphic to $H$. The $(a,d)-H$ antimagic covering on the G graph is a biijective functin of $f:V(G)\cup E(G) \rightarrow \{1,2,...,|V(G)|+|E(G)|\}$ till all of the $H'$ subgraphs that isomorphic to H have weight $w(H)=\sum_{v\epsilon V(H')}f(v)+\sum_{e\epsilon E(H')}f(e)$ from an arithmatic sequence $\{a,a+d,a+2d,...,a+(t-1)d\}$, where $a$ and $d$ is the positive integres and $t$ is the number of all subgraphs $H'$ isomorphic to $H$. Such a labeling is called super if $f:V(G)\rightarrow \{1,2,...,|V(G)|\}$. This research aims to determine the super $(a, d)-S_3$ antimagic total decomposition of Helm graph and also we will use it to develop \textit{chipertext} from a secret message.