Antimagic Labeling on Spiders
Date Issued
2015
Date
2015
Author(s)
Huang, Tzu-Yen
Abstract
Let G be a simple finite graph with n vertices and m edges. A labeling of G is a bijection from the set of edges to the set {1, 2, · · · ,m} of integers. Given a labeling of G, for each vertex, its vertex sum is defined to be the sum of labels of all edges incident to it. If all vertices have distinct vertex sums, we call this labeling antimagic. Suppose f is an antimagic labeling of G, and for any two vertices u, v with deg(u) < deg(v), if vertex sum of u is strictly less than vertex sum of v, then we say f is a strongly antimagic labeling of G. Furthermore, a graph G is said to be (strongly) antimagic if it has (a strongly) an antimagic labeling. The concept of antimagic labeling was first introduced by Hartsfield and Ringel. In their book, they not only proved that some graphs such as cycles, paths, wheels, complete graphs etc are antimagic, but also conjectured that all connected graphs other than K2 are antimagic. In the past years, graphs with some restriction were gradually poven to be antimagic, but this conjecture is still widely open. In this thesis, we restrict our graphs to spiders, which is a graph with a core and at least three legs, each leg contains some edges. Since all spiders have already been proven to be antimagic, we will prove a stronger result here, that is, all spiders are strongly antimagic. In the last chapter, we will discuss whether some variation of spiders are antimagic or not.
Subjects
antimagic
strongly antimagic
labeling
spider
Type
thesis
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