Rectangle-Visibility Representation of Products of Graphs

Inhaltsverzeichnis (Table of Contents)

• Introduction
  • Background of the Study
  • Rationale of the Project
  • Overview of the Project
• Literature Review
• Preliminaries
  • Definitions
• Products of Graphs as Rectangle-Visibility Graphs
  • Definitions of the types of Graph Products
  • Cartesian Product
  • Direct Product
  • Strong Product
• Conclusion

Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)

This essay explores the representation of products of different graph classes as rectangle-visibility graphs (RVGs), specifically focusing on Cartesian, direct, and strong products. It aims to provide constructive proofs for obtaining linear-time layouts of these graph products as RVGs.

• Representation of graph products as RVGs
• Linear-time layout algorithms for RVGs
• Cartesian, direct, and strong products of graphs
• Rectangle-visibility graphs and their properties
• Applications of RVGs in various fields

Zusammenfassung der Kapitel (Chapter Summaries)

• Introduction: This chapter provides a background on visibility representation of graphs, explaining the concept and its application in representing graph products. It outlines the rationale for the project, highlighting the importance of exploring RVGs for graph products, and gives an overview of the topics covered in the essay.
• Literature Review: This chapter reviews existing literature on visibility representation of graphs and relevant concepts related to graph products and RVGs. It explores previous studies and research findings, setting the context for the current work.
• Preliminaries: This chapter provides essential definitions and concepts related to graph theory and RVGs. It introduces key definitions and terminology that are used throughout the essay.
• Products of Graphs as Rectangle-Visibility Graphs: This chapter delves into the main focus of the essay, examining the representation of different graph products as RVGs. It explores the specific types of graph products (Cartesian, direct, and strong), providing constructive proofs and illustrating the linear-time layout algorithms.

Schlüsselwörter (Keywords)

Key terms and concepts in this essay include: rectangle-visibility graph (RVG), cartesian product, direct product, strong product, graph products, visibility representation, linear-time layout, constructive proofs.