studyhubGraph Theory

Three lecture decks, as problems you have to solve.

Nine modules, every one auto-graded, every one generating 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.

  1. 01

    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, adjacent vs incident.

    not started

  2. 02

    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.

    not started

  3. 03

    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.

    Q1, Q2 · 4–6 marks · not started

  4. 04

    Walks, Trails & Paths

    Click a vertex sequence to satisfy a spec — including specs where the honest answer is “does not exist”.

    Q4, Ex 5 · 4 marks · not started

  5. 05

    Subgraph Surgery

    Produce G − X, G − U and the induced subgraph G[S]. The induced case is where marks quietly disappear.

    Ex 4 · 4 marks · not started

  6. 06

    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.

    Ex 1–3 · 9 marks · not started

  7. 07

    Degree & Handshake

    The First Theorem of Graph Theory under time pressure: counting problems, parity arguments, pseudograph loops, indegree and outdegree.

    Ex 3 · 4 marks · not started

  8. 08

    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.

    Ex 1 · 21 marks · not started

  9. EX

    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.

    no attempts

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