D-ANTIMAGIC LABELING ON ORIENTED GRAPHS

• Main Author: Muchlas Abrar, Ahmad
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/74548
• Institution: Institut Teknologi Bandung

Let ??G be an oriented graph with vertex set V ( ??G ) and arc set A( ??G ). Suppose that D ? {0, 1, 2, . . . , ?} is a distance set where ? = max{d(u, v) < ?|u, v ? V ( ??G )}. Given a bijection h : V ( ??G ) ? {1, 2, , . . . , |V ( ??G )|}, the D-neighborhood weight of a vertex v ? V ( ??G ) is defined as ?D(v) = P u?ND(v) h(u), where ND(v) = {u ? V |d(v, u) ? D}. A labeling h is called a D-antimagic labeling if for every pair of distinct vertices x and y, ?D(x) ?= ?D(y). An oriented graph ??G is called D-antimagic if ??G contains such labeling. In this thesis, we study the existences and characteristics of orientations on paths, cycles, complete bipartite graphs, and complete multipartite graphs such that those graphs admit D-antimagic labelings.