Ryscha Nurzulia Budi Pratiwi, Purwanto
Let H and G be finite graphs where every edge of G belongs to at least one subgraph of G that is isomorphic to H. An (a,d) - H - antimagic total labeling of a graph G is a bijection f: V(G) ∪ E(G) → {1,2,..., │V(G)│+│E(G)│} such that for all subgraphs H' isomorphic to H, the H' - weights, F(H')= ςv∈V(H') f(v) + ςe∈E(H') f(e), form an arithmetic progression {a, a + d,.., a + (k - 1)d}, where a is a positive integer, d is a nonnegative integer, and k is the number of subgraphs of G isomorphic to H. If the vertex set V(G) receives the minimum possible labels {1,2,.., │V(G)│}, then f is called a super (a,d) -H -antimagic total labeling. In this paper we study super (a,d) - C4 -antimagic total labeling of graph P4 × Pn. We find that the graph P4 × Pn has a super (34n + 4, 2) - C4 - antimagic total labeling when a = 34n + 4 and d = 2 or when a = 32n + 4 and d = 4. © 2024 Author(s).
Department of Mathematics, Universitas Negeri Malang, Jl. Semarang 5, Malang, 65145, Indonesia
