Further Maths - Graphs
Pearson Edexcel Further Mathematics 2022
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Flashcards
Vertices and degree
What is the sum of degrees of all vertices in a graph?
Double the number of edges.
Isomorphic graphs
What is the property called when two graphs have the same vertices and edges?
They are isomorphic.
What is true about all these graphs?How can you show two graphs are isomorphic?
Match up vertex degrees and the edge set.
Walks, trails, paths and cycles
What is a walk in relation to graphs?
A sequence of edges where the end vertex of one edge is the start vertex of the next.
What is a path in relation to graphs?
A trail where none of the vertices are repeated.
What is a cycle or circuit in relation to graphs?
A path that joins back up to the beginning.
Simple, connected graphs and trees
Why is this graph not simple?What does it mean for two vertices to be connected?
There is a path between them.
What does it mean for a graph to be connected?
All pairs of vertices are connected.
Complete and planar graphs
What is a complete graph?
One in which every possible pair of vertices is connected by an edge.
What is the formula for the number of edges for $K _ n$ (the complete graph with $n$ vertices)?
What is a planar graph?
A graph that can be drawn so that none of the arcs cross.
Ordering the ways to traverse a graph
What is the order of the 4 ways you can get around a graph, going from least restrictive to most restrictive?
- Walk
- Trail
- Path
- Cycle
Defining a graph and loops
Bipartite graphs
What is a bipartite graph?
Graphs that consist of two or more independent sets of vertices that have no connections between themselves.
What is this an example of?Revisiting trails, paths and cycles
How can you remember that a trail is where no edge is visited more than once?
It’s an “Eulerian trail”, not “Eulerian path”.