| dc.description.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. | en_US |
