The Application of Super $(a,d)-$Edge Antimagic Total Decomposition of Shackle of Antiprism Graph in Developing A Ciphertext

Abstract

All graphs in this paper are finite, simple, and undirected. A graph $G$ is said to be an super $(a,d)-H$ antimagic total labeling by $H-$decomposition if there exist a bejective function $f:V(G)\cup E(G)\rightarrow\{1,2,3,…,|V(G)|+|E(G)|\}$ such that for all subgraphs $H'$ isomorphic to $H$, the total $H'$-weights $w(H')=\sum_{v\in V(H')}f(v)+\sum_{e\in E(H')}f(e)$ from an arithmetic sequence $\{a,a+d,a+2d,…,a+(s-1)d\}$, where $a$ and $d$ are positive integers and $s$ is the number of all subgrabs $H^i$ isomorphic to $H$. Such a labeling is called super if $f:V(G)\rightarrow\{1,2,…,|V(G)|\}$. In this paper we will study the existence super $(a,d) - H-$antimagic total decompotition of shackle of antiprism graph and use it to develop a polyalphabetic chiper.