Lectures 1–3, 5–9 · auto-graded, a fresh problem every time

Eight lecture decks, as problems you have to solve.

Every module is auto-graded and generates a fresh problem each time, so you cannot memorise an answer key. Weighted toward the drawing-and-justifying questions that carry the marks on your exercise sheets.

Modules

Every one marked, every one a new problem each time.

13 modules + exam

01Lec 1–9
Definition Traps
Rapid-fire questions built on the exact confusions that lose marks: walk vs trail vs path, circuit vs cycle, subgraph vs induced vs spanning, bridge vs cut-vertex, minimal vs minimum edge-cut, Kruskal vs Prim.
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02Lec 1–3
Graph Inspector
Read a graph cold and report n, m, δ, Δ, degree sequence, k(G), distance, diameter and bipartiteness. Every field must be right.
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03Lec 1 · Q1, Q2 · 4–6 marks
Edge-Set Builder
Build E(G) by hand for number-set graphs (i+j ∈ S or |i−j| ∈ S) and word graphs. New set every time.
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04Lec 1 · Q4, Ex 5 · 4 marks
Walks, Trails & Paths
Click a vertex sequence to satisfy a spec — including specs where the honest answer is “does not exist”.
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05Lec 1 · Ex 4 · 4 marks
Subgraph Surgery
Produce G − X, G − U and the induced subgraph G[S]. The induced case is where marks quietly disappear.
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06Lec 2 · Ex 1–3 · 9 marks
Classes & Operations
Kₙ, Cₙ, Pₙ, K_{s,t}, complements, bipartiteness, distance and diameter — plus G ∪ H, the join G + H and the Cartesian product G × H.
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07Lec 3 · Ex 3 · 4 marks
Degree & Handshake
The First Theorem of Graph Theory under time pressure: counting problems, parity arguments, pseudograph loops, indegree and outdegree.
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08Lec 3 · Ex 1 · 21 marks
Construction Challenges
Draw a graph meeting a spec — or prove it cannot exist. This is Exercise 1, the biggest single block of marks on the sheet.
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09Lec 5 · Midterm Q3, Q4, Q6
Isomorphism
Decide whether two graphs are isomorphic. If they are, give the vertex-bijection; if not, name the invariant they disagree on — the same degree sequence is never proof. Exam-style mode adds decks of cards and drawing every non-isomorphic graph.
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10Lec 6 · Midterm Q2a, Q8, Q9
Bridges & Trees
Mark every bridge of a graph, and recover a tree's missing degree counts from its order — Theorem 6.4 does the rest. Exam-style mode adds spanning trees and the fewest edges that kill every bridge.
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11Lec 7 · Midterm Q7
Minimum Spanning Trees
Run Kruskal's and Prim's Algorithms by hand on a weighted graph, edge by edge in the order they choose, then give w(T).
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12Lec 8 · Midterm Q1, Q2b–c
Cut-Vertices & Blocks
For a graph G, determine the cut-vertices, the bridges and the blocks — all three on one figure, all three marked. Exam-style mode adds Question 1's parts and drawing a block.
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13Lec 9 · Midterm Q1, Q10, Q19
Connectivity κ and λ
Give κ(G), λ(G) and δ(G), then back the number up by marking a minimum vertex-cut or edge-cut on the graph. Exam-style mode adds the street-repairs problem.
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EXLec 1–9
Exam Simulator
A timed mixed paper drawn from every module, marked the way your exercise sheets are marked, with a per-topic breakdown at the end telling you exactly what to revise next.
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Eight lecture decks, as problems you have to solve.

Modules

Definition Traps

Graph Inspector

Edge-Set Builder

Walks, Trails & Paths

Subgraph Surgery

Classes & Operations

Degree & Handshake

Construction Challenges

Isomorphism

Bridges & Trees

Minimum Spanning Trees

Cut-Vertices & Blocks

Connectivity κ and λ

Exam Simulator

Reference

Cram sheet

Flashcards

Formula sheet