DISTANCE ANTIMAGIC LABELING OF GRAPH PRODUCTS
A graph G with order n is called distance antimagic if there exists a bijection from the set of vertices to the set of integers 1,2,…,n such that all vertex sums are pairwise distinct, where a vertex sum is the sum of maps of all vertices ajacent with that vertex. According to Kamatchi-Arumugam&#...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/20867 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A graph G with order n is called distance antimagic if there exists a bijection from the set of vertices to the set of integers 1,2,…,n such that all vertex sums are pairwise distinct, where a vertex sum is the sum of maps of all vertices ajacent with that vertex. According to Kamatchi-Arumugam's conjecture, every graph without two vertices having the same neighborhood is distance antimagic. <br />
Hefetz proved that every graph on 3^k vertices for some positive integer k is antimagic. The main tool used in his proof is the Combinatorial Nullstellensatz. We adopt his proof to distance antimagic labeling, that is for union of K_3 on 3^k vertices. The proof is written in this book as an example of application of Combinatorial Nullstellensatz to distance antimagic labeling. In this book, we present results on distance antimagic labeling for products of graphs. Our main tool is by arranging labels of the product graph based on their base graphs. <br />
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