Flashcards
Graphs
Cards in this deck (23)
- 1GraphA finite set of points connected by lines
- 2EdgeJoins one vertex to another, or starts and ends at the same vertex (a loop)
- 3SimpleNo loops or multiple edges
- 4ConnectedEvery vertex is connected by a single edge or sequence of edges to every other vertex
- 5DisconnectedCan be separated into two separate 'pieces'
- 6CompleteEvery vertex is connected to every other vertex by one edge
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Denoted K - 7SubgraphPart of a graph which is itself a graph
- 8PlanarA graph which can be drawn without any edges crossing over
- 9Degree (Vertex)The number of edges which start or finish at a vertex (count loops twice)
- 10Handshaking TheoremΣ(degrees of vertices) = 2 (number of edges)
- 11DigraphA graph whose edges have a direction
- 12BipartiteA graph with two discrete sets of vertices, with no edges connective vertices in the same set
- 13Complete BipartiteA bipartite graph in which every vertex in one set is connected to every vertex in the other set by one edge
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Denoted K - 14IsomorphicIdentical graphs which have been drawn in different orientations
- 15WalkA sequence of edges and vertices in which the end of one edge is the beginning of the next
- 16TrailA walk with no repeated edges (in either direction)
- 17PathA walk with no repeated vertices (except that the first may be the last)
- 18CycleA closed walk, trail or path
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Finishes at the same vertex where it started - 19Eulerian TrailCrosses every edge of a graph exactly once
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Has no vertices with an odd degree - 20Semi-EulerianHas only two odd vertices; only transversible if you start and finish at the odd vertices
- 21Hamiltonian CycleA closed path which passes through every vertex of a graph
- 22TreeA connected graph which contains no cycles
- 23Spanning TreeA subgraph which includes all vertices of the original graph, and is also a tree
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- A level Further Maths Flashcards on Graphs, created by Nathanael Jenkins on 04/05/2019.
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- Nathanael Jenkins
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