What’s on the Graph Vocabulary poster
A definition and 7 facts worth remembering.
A graph is a set of vertices together with a set of edges, each joining a pair of them.
- Degree of a vertex is the number of edges at it
- Handshake lemma: the degrees sum to twice |E|
- A tree is connected and acyclic, so |E| = |V| − 1
- Bipartite exactly when there is no odd cycle
- The complete graph on n vertices has n(n − 1)/2 edges
- A simple planar graph obeys |E| ≤ 3|V| − 6
- Euler: |V| − |E| + |F| = 2 when connected and planar
- Edges in a complete graph — n(n − 1)/2
- Edges in a tree — |V| − 1
- Sum of all degrees — 2|E|
- The number of odd-degree vertices in any graph is always even.
Kuratowski: a graph is planar exactly when it contains no subdivision of K₅ or of the complete bipartite K(3, 3).
Questions about the Graph Vocabulary poster
- What’s on the Graph Vocabulary poster?
- A definition and 7 facts worth remembering. A graph is a set of vertices together with a set of edges, each joining a pair of them. Degree of a vertex is the number of edges at it; Handshake lemma: the degrees sum to twice |E|; A tree is connected and acyclic, so |E| = |V| − 1; Bipartite exactly when there is no odd cycle; The complete graph on n vertices has n(n − 1)/2 edges; A simple planar graph obeys |E| ≤ 3|V| − 6; Euler: |V| − |E| + |F| = 2 when connected and planar; Edges in a complete graph — n(n − 1)/2; Edges in a tree — |V| − 1; Sum of all degrees — 2|E|; The number of odd-degree vertices in any graph is always even.. Kuratowski: a graph is planar exactly when it contains no subdivision of K₅ or of the complete bipartite K(3, 3).
- Who is the Graph Vocabulary poster for?
- Graph Vocabulary belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning discrete mathematics can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Graph Vocabulary poster?
- Before any graph proof: fix what degree, tree, bipartite and planar actually mean. A wall chart earns its place by being glanceable from where the work is happening, so Graph Vocabulary belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Graph Vocabulary?
- The Binomial Theorem, Counting Principles and Euler & Hamiltonian Paths sit alongside Graph Vocabulary in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Binomial TheoremCounting PrinciplesEuler & Hamiltonian Paths
- Is the Graph Vocabulary poster free to download and print?
- Yes. Graph Vocabulary downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Graph Vocabulary poster print at?
- Graph Vocabulary is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Graph Vocabulary loses nothing.Printing guide
Related posters
Charts that sit alongside Graph Vocabulary on the same wall.
Browse every Mathematics poster, or start from the full catalogue.