Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext

Abstract

Let Hi be a finite collection of simple, nontrivial and undirected graphs and let each Hi have a fixed vertex vj called a terminal. The amalgamation Hi as vj as a terminal is formed by taking all the Hi’s and identifying their terminal. When Hi are all isomorphic graphs, for any positif integer n, we denote such amalgamation by G = 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) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights w(H) = P v∈V (H) P f(v)+ e∈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 = Amal(H, v, n) and its disjoint union when H is a complete graph.