# Terminology for Graph Theory

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Graph
Collection of vertices & edges.
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Vertex/Node
The dots in a graph (usually where 2 or more edges meet, but not necessarily).
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Edge/Arc
A line between two vertices.
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Tree
A graph with no cycles.
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Order (degree) of a vertex or Valency
The number of edges starting or finishing at that vertex.
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Simple graph
A graph with no loops or multiple edges.
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A path
A route from one vertex to another which does not repeat any edge.
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A cycle
A route starting and finishing at the same vertex.
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Connected graph
A graph in which there is a route from each vertex to any other vertex.
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Complete graph
A simple graph in which every pair of vertices is connected by an edge.
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Bipartite graph
One in which the vertices are in two sets and each edge has a vertex from each set.
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Planar graph
One which can be drawn with no edges crossing.
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Sub graph
Any set of edges & vertices taken from a graph is a sub-graph.
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Hamiltonian cycle
A cycle that visits every vertex of the graph.
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Eulerian cycle
A cycle that travels along every edge of the graph.
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Eulerian graph
A gaph with no odd verticles.
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Di-graph
A graph in which the arcs have a particular direction.
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Spanning tree
A subgraph of a graph which includes all the vertices of the graph and is also a tree.
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Minimum spanning tree
A spanning tree such that the total length of edges is as small as possible.
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## Other cards in this set

### Card 2

#### Front

The dots in a graph (usually where 2 or more edges meet, but not necessarily).

Vertex/Node

### Card 3

#### Front

A line between two vertices.

### Card 4

#### Front

A graph with no cycles.

### Card 5

#### Front

The number of edges starting or finishing at that vertex.