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Chapter One
Notation, maps, and some graph families |
Week 1 |
§1.1 – Graphs §1.2 – Subgraphs §1.3 – Automorphisms (slides for 1.1-3) |
| Week 2 |
§1.4 – Homomorphisms §1.5 – Circulant graphs §1.6 – Johnson graphs (slides for 1.4-6) |
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| Week 3 |
§1.7 – Line graphs
(slides for 1.7) §1.8 – Planar graphs (slides for 1.8) |
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| Homework One |
Due Jan 29 |
8 problems from Chapter 1 |
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Chapter Two
Group actions, symmetry, orbitals, and primitivity |
Week 4 |
§2.1 – Permutation groups §2.2 – Counting (slides for 2.1-2) |
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Week 5 |
§2.3 – Asymmetric graphs (slides for 2.3a), (slides for 2.3b) §2.4 – Orbits on pairs (slides for 2.4) |
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Week 6 |
§2.5 – Primitivity
(slides for 2.5) §2.6 – Primitivity & connectivity (slides for 2.6) |
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| Homework Two |
Due Feb 19 |
8 problems from Chapter 2 |
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Chapter Three
Transitivity and connectivity |
Week 7 |
§3.1 – Vertex-transitive graphs §3.2 – Edge-transitive graphs (slides for 3.1-2) §3.3 – Edge connectivity (slides for 3.3) |
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Week 8 |
§3.4 – Vertex connectivity §3.5 – Matchings §3.6 – Hamiltonian Paths & Cycles |
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Week 9 |
§3.7 – Cayley graph characterization §3.8 – Non-Hamiltonian Cayley digraphs |
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Week 10 |
§3.9 – Retracts §3.10 – Transpositions |
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| Homework Three |
Due Mar 18 |
8 problems from Chapter 3 |
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