D-ANTIMAGIC LABELING FOR HYPERCUBES

• Main Author: Finan Hernawan, Rivary
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/46381
• Institution: Institut Teknologi Bandung

Let G = (V;E) be a graph with order n, and let f : V (G) ! f1; 2; :::; ng be a bijection. Define a distance set, D f0; 1; 2; : : : ; diam(G)g. For each vertex v 2 V (G), the sum of its D-neighborhood labels u2ND(v)f(u) is called as the D- weight of v denoted by wD(v). If wD(x) 6= wD(y), for each two distinct vertices x and y, then f is also called as D-antimagic labeling. The objective of this thesis is to find various distance sets D such that a hypercube admits a D-antimagic labeling. Our method is by recursively constructing D-antimagic labelings based on a labeling for hypercubes with smaller dimension. We also construct an algorithm to determine all distance sets D such that a graph G admits a D-antimagic labelling.