Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext - Hani'ah Zakin; Ika Hesti Agustin; Kusbudiono Kusbudiono; Dafik Dafik (CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS, 2021)
Let ${H_i}$ be a finite collection of simple, nontrivial and undirected graphs and let each $H_i$ have a fixed vertex $v_j$ called a terminal. The amalgamation $H_i$ as $v_j$ as a terminal is formed by taking all the $H_i$'s and identifying their terminal. When $H_i$ are all isomorphic graphs, for any positif integer $n$, we denote such amalgamation by $G={\rm Amal}(H,v,n)$, where $n$ denotes the number of copies of $H$. The graph $G$ is said to be an $(a, d)$-$H$-antimagic total graph if there exist a bijective function $f: V(G) \cup E(G) → \{1, 2,… ,|V (G)| + |E(G)|\}$ such that for all subgraphs isomorphic to $H$, the total $H$-weights $w(H)= \sum_{v\in V(H)}f(v)+\sum_{e\in E(H)}f(e)$ form an arithmetic sequence $\{a, a + d, a +2d,...,a+(t - 1)d\}$, where $a$ and $d$ are positive integers and $t$ is the number of all subgraphs isomorphic to $H$. An $(a,d)$-$H$-antimagic total labeling $f$ is called super if the smallest labels appear in the vertices. In this paper, we study a super $(a, d)$-$H$ antimagic total labeling of $G={\rm Amal}(H,v,n)$ and its disjoint union when $H$ is a complete graph.