Graphs practice, graded like a real exam
Terminology, connectivity, trees, paths and cycles. Graphs rewards precision and repetition more than almost anything else on a discrete structures course — it is exactly the kind of topic where working through twenty varied problems beats re-reading the chapter a third time. QED gives you an endless supply of exam-grade graphs questions and marks every answer the way an examiner would, so each attempt actually teaches you something.
✓ First questions free · no card · no setup
What a Graphs question looks like
In a QED session, an exam-level graphs question might ask you to apply the handshake lemma, decide whether a graph has an Euler or a Hamilton circuit, use the tree identity |E| = |V| − 1, or test two graphs for isomorphism.
Every question carries a hidden marking rubric. You answer in real notation, and QED marks each criterion separately — awarding partial credit and showing a full worked solution, so you learn from the marks you dropped.
Every Graphs subtopic
14 focused guides, each with the method, a worked example and the mistakes that cost marks. Work through them in order or jump to your weak spot.
- 1Degrees & the handshake lemma
- 2Paths, cycles, connectivity & components
- 3Trees & their properties
- 4Bipartite graphs & colouring basics
- 5Euler & Hamilton paths and circuits
- 6Adjacency matrices & isomorphism
- 7Degree sequences & graphic sequences
- 8Spanning trees: Kruskal & Prim
- 9Shortest paths with Dijkstra
- 10Planarity & Euler’s formula
- 11Directed graphs, in-degree & out-degree
- 12Binary trees: height, traversals & counting
- 13Chromatic number & colouring bounds
- 14Matchings & Hall’s marriage theorem
Why students use QED for Graphs
Not another chatbot that blesses whatever you type. QED is built for deliberate practice — the way maths actually sticks.
Practice that never runs out
A textbook gives you a handful of graphs exercises with the same worked answers everyone has seen. QED generates unlimited fresh graphs questions at warm-up, exam and challenge level, so you can drill a weak spot until it is automatic — not until you run out of problems.
Marked like an examiner, not a checkbox
Most tools just say “correct” or “wrong”. QED marks your graphs answer against a point-by-point rubric, awards partial credit, shows exactly where the reasoning slipped, and gives a full model solution. A right answer with the wrong argument still loses the argument marks — just like a real exam.
A library you can come back to
Every graphs question you generate is saved, organised and re-takeable as a timed exam. Your mastery is tracked per topic, so you always know whether Graphs is exam-ready or still needs work — and you can export any question or exam report to PDF.
Write maths the way you actually write it
Answer in real notation with a one-tap symbol palette and a visual equation editor, drop in truth tables, or photograph a handwritten page — QED converts your handwriting to clean LaTeX. No fighting with syntax to show what you know.
How practising Graphs works
- Generate a fresh questionPick Graphs and a difficulty — warm-up to build intuition, exam level for the real thing, or challenge for multi-step problems. A new, verified question appears in seconds.
- Answer in real notationType it, build it in the equation editor, lay out a truth table, or photograph your handwritten working and let QED convert it to LaTeX.
- Get marked criterion by criterionQED scores every rubric point separately, awards partial credit, flags where the reasoning slipped and shows a full model solution. The question is saved to your library to retake any time.
Related topics
Building a full picture of discrete structures? These pair naturally with Graphs.
Graphs — frequently asked questions
Is QED good for revising Graphs before an exam?
Yes — that is exactly what it is built for. Generate graphs questions at exam level (or push up to challenge), answer them under timed exam mode, and get marked against a rubric with a full model solution. You can retake any question and watch your Graphs mastery climb until it is solid.
How many Graphs questions can I practise?
As many as you like. QED generates fresh graphs problems on demand instead of recycling a fixed set, and every question you make is saved to your library to retake for free. New accounts start with free question generations, no card required.
Do I need to know LaTeX to answer Graphs questions?
No. There is a one-tap palette for symbols, a visual equation editor, and a truth-table builder — and you can photograph a handwritten solution and let QED convert it to LaTeX for you. You concentrate on the maths, not the typesetting.
Ready to make Graphs exam-proof?
Generate your first graphs questions free — no card, no setup. Practise until it is second nature.
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