Super (a,d)-edge Antimagic Total Labeling of\\ Shackle ($F_6, B_2, n$) for Developing a Polyalphabetic Cryptosystem

Abstract

A graph $G$ of order $p$ and size $q$ is called an $(a,d)$-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 is called super if the smallest possible labels appear on the vertices. In this paper we study a super edge-antimagic total labeling of Graph Shackle ($F_6, B_2, n$) and we will use it to develop a polyalphabetic cryptosystem.