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The Planar Cubic Cayley Graphs.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2018Copyright date: ©2017Edition: 1st edDescription: 1 online resource (94 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470442040
Subject(s): Genre/Form: Additional physical formats: Print version:: The Planar Cubic Cayley GraphsDDC classification:
  • 511/.5
LOC classification:
  • QA166.145 .G467 2017
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introductory material and basic facts -- 1.1. Introduction -- 1.2. Definitions -- 1.3. Known facts -- 1.4. General facts regarding connectivity -- 1.5. Graphs of connectivity 1 or 2 -- 1.6. Crossings of \mpsc s -- Chapter 2. The finite and 1-ended cubic planar Cayley graphs -- Chapter 3. The planar multi-ended Cayley graphs with 2 generators -- 3.1. Graphs with monochromatic cycles -- 3.2. Graphs without monochromatic cycles -- Chapter 4. The planar multi-ended Cayley graphs generated by 3 involutions -- 4.1. Graphs with 2-coloured cycles -- 4.2. Graphs without 2-coloured cycles -- Chapter 5. Outlook -- Acknowledgements -- Bibliography -- Back Cover.
Summary: The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
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Cover -- Title page -- Chapter 1. Introductory material and basic facts -- 1.1. Introduction -- 1.2. Definitions -- 1.3. Known facts -- 1.4. General facts regarding connectivity -- 1.5. Graphs of connectivity 1 or 2 -- 1.6. Crossings of \mpsc s -- Chapter 2. The finite and 1-ended cubic planar Cayley graphs -- Chapter 3. The planar multi-ended Cayley graphs with 2 generators -- 3.1. Graphs with monochromatic cycles -- 3.2. Graphs without monochromatic cycles -- Chapter 4. The planar multi-ended Cayley graphs generated by 3 involutions -- 4.1. Graphs with 2-coloured cycles -- 4.2. Graphs without 2-coloured cycles -- Chapter 5. Outlook -- Acknowledgements -- Bibliography -- Back Cover.

The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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