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# AQA COMP3 Graphs

### Definitions about General graph theory not in the Textbook

TermDefinition
Graph A finite, discrete set of vertices linked by edges
Tree A connected, undirected graph with no cycles
Rooted tree A tree where one vertex is the starting point, and all points use this as a ‘root’
Directed graph A graph where each edge has a direction (shown by an arrow)
Vertex A point where two edges connect
Edge A line connecting two vertices
Neighbours Adjacent vertices to a vertex
Degree (of a vertex) The number of edges connected to a vertex
Weighted graph A graph where each edge has been given a weight
Simple graph A graph where there are no loops, and no more than 1 edge per vertex. Each edge connects two different vertices.
Path A route that does not have to visit all edges
Circuit A succession of edges that start and end at the same vertex
Cycle A closed path where all the edges and intermediate vertices are different
Undirected graph A graph with no direction (ie an edge can be traversed either way)
Explorer’s problem The solution finds a route that traverses each ‘road’ (edge) exactly once before returning to the start point
Traveller’s problem The solution finds a route that visits each ‘city’ (vertex) exactly once before returning to the start point
Created by: joemch