The Planar Cubic Cayley Graphs.
Georgakopoulos, Agelos.
The Planar Cubic Cayley Graphs. - 1st ed. - 1 online resource (94 pages) - Memoirs of the American Mathematical Society ; v.250 . - Memoirs of the American Mathematical Society .
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.
9781470442040
Cayley graphs.
Graph connectivity.
Graph theory.
Electronic books.
QA166.145 .G467 2017
511/.5
The Planar Cubic Cayley Graphs. - 1st ed. - 1 online resource (94 pages) - Memoirs of the American Mathematical Society ; v.250 . - Memoirs of the American Mathematical Society .
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.
9781470442040
Cayley graphs.
Graph connectivity.
Graph theory.
Electronic books.
QA166.145 .G467 2017
511/.5