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D1 Definitions
Graph Definitions
| Question | Answer |
|---|---|
| Graph | a set of vertices (or nodes) together with a set of edges |
| Edge | a line with a vertex at each end |
| Loop | an edge with the same vertex at each end |
| Degree (or Order) of a Vertex | the number of edges incident on it |
| Simple Graph | a graph where there are no loops, and in which there is no more than one edge connecting any pair of vertices |
| Walk | a sequence of edges in which the end of one edge (except the last) is the beginning of the next |
| Trail | a walk where no edge is repeated |
| Path | a trail where no vertex is repeated |
| Cycle | a closed path |
| Hamiltonian Cycle | a cycle which visits every vertex |
| When is a graph connected? | if a path exists between every pair of vertices |
| Tree | a simple connected graph with no cycles |
| Digraph (directed graph) | a graph is which at least one edge has a direction associated with it |
| Complete graph | a simple graph in which every pair of vertices is connected by an edge |
| Incidence Matrix | a way of representing a graph by a matrix |
| Isomorphic Graphs | Two graphs are isomorphic if one can be stretched, twisted or otherwise distorted into each other |
| Planar Graph | a graph which can be drawn without any edges crossing |
| Bipartite Graph | a graph in which the vertices fall into two sets and in which each edge has a vertex from one set at one end and from the other set at its other end |
Created by:
Masterniket
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