- Title
- Graph labeling techniques
- Creator
- Tanna, Dushyant
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2017
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- We give some background to the labeling schemes like graceful, harmonious, magic, antimagic and irregular total labelings. Followed by this we give some preliminary results and open problems in these schemes. We will introduce a new branch of irregular total labeling, irregular reflexive labeling. This new labeling technique has few variations on vertices labels from irregular total labeling. They are, 1) The vertices labels are non negative even integers. 2) The vertex label 0 is permissible, representing the vertex without loop. The vertex (edge) irregular reflexive labeling is a total irregular labeling with above conditions on vertices labeling such that the vertices (edges) weights are distinct. The idea is to use minimum possible labels for vertices (edges) and thus keeping the reflexive vertex (edge) strength as low as possible. We believe that this new technique is closer in concept to the original irregular labeling as proposed by Chartrand et al., since the vertex labels are also being used to represent edges(loops). Again the objective is to minimize the total strength by using the smallest vertices/edges labels. We will give edge and vertex irregular reflexive strengths for many graphs such as paths, cycles, stars, complete graphs, prisms, wheels, baskets, friendship graphs, join of graphs and generalised friendship graphs and present labeling techniques for these graphs. We also describe edge covering, H-edge covering, H-magic and H-antimagic graphs and prove some theorems based on these concepts. Many results have been established for construction of H-antimagic labelings of graphs. We will use the partitions of a set of integers with determined differences, the upper bound of the difference d if the graph GH is super (a,d)-H-antimagic, establishment of connection between H-antimagic labelings and edge-antimagic total labelings. We have also posed some open problems. Finally we address why study of graph labeling is important by explaining some applications of graph labeling and give some open problems and conjectures.
- Subject
- graph theory; vertices; graph labeling; combinatorics
- Identifier
- http://hdl.handle.net/1959.13/1354312
- Identifier
- uon:31249
- Rights
- Copyright 2017 Dushyant Tanna
- Language
- eng
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