Pelabelan Total Super ($a,d$) - Face Antimagic dari Graf Shackle ($C_5,e,n$)

Abstract

Let $G$ be a simple graph of order $p$, size $q$ and face $r$. The graph $G$ is called a super ($a,d$) - face antimagic total labeling , if there exist a bijection $f:V(G)\cup E(G)\cup F(G)$ $\rightarrow \{1,2,...,p+q+r\}$ such that the set of $s$-sided face weights, $W_{s} = \{a_{s},a_{s}+d,a_{s}+2d,...,a_{s}+(r_{s}-1)d\}$ form an arithmetic sequence with first term $a$,common difference $d$, where $a$ and $d$ are positive integers $s$ and $r_{s}$ is the number of $s$-sided faces. Such a graph is called super if the smallest possible labels appear on the vertices. The type of Face Antimagic Labeling is (1,1,1). In this paper we will study a Super $(a,d)$ - Face Antimagic of Shackle ($C_5,e,n$) Graph and we will use it to develop a polyalphabetic chyptosystem.