Super Edge Antimagic Total pada Generalisasi Shackle Graf Kipas dan Aplikasinya dalam Pengembangan Cryptosystem

Abstract

A graph $G$ of order $p$ and size $q$ is called an {\it $(a,d)$-edge-antimagic total} if there exist a bijection $f : V(G)\cup E(G) \to \{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic sequence with first term $a$ and common difference $d$. Such a graph $G$ is called {\it super} if the smallest possible labels appear on the vertices. In this paper we will study the exsistence of super (a,d)-edge antimagic total labeling of shackle of fan, denoted by $ {\rm shack}(F_6,c_4^1,n)$, and the application of developing of polyalphabetic cryptosystem. The result shows that connected shackle of fan admits a super $(a,d)$-edge antimagic total labeling for $d=0,1,2$, and it can be used to develop a secure polyalphabetic cryptosystem.