# Decision Graph Definitions

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Arc (Edge)
A line connecting two nodes (vertices) on a graph
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Bipartite Graph
Vertices fall into two sets and each edge has a vertex with one set at one end and the other set at the other end.
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Complete graph
simple graph in which every pair of vertices is connected by an edge.
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Connected graph
Where a path exists between every pair of vertices.
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Cycle
A closed path
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Degree
The degree (or order) of a vertex is the number of arcs (edges() connecting to it
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Digraph
Graph in which at least one arc ((edge) has a direction associated with it.
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Discrete set
A set which can be counted
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Graph
A set of vertices linked in some way with arcs (edges)
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Hamilton cycle
A cycle which visits every vertex. Each vertex is visited once and only once.
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Incidence matrix
A way of representing a graph on a matrix.
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Isomorphic
Two graphs are isomorphic if one can be stretched, twisted or otherwise distorted into the other
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Loop
An arc whose beginning and end both link to the same vertex.
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Vertex (Node)
A point on a graph that is connected to other vertices by arcs.
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Path
A trail in which no vertex is repeated
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Planar graph
A graph which can be drawn with any arcs crossing
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Simple graph
A graph in which tehre are no loops and in which there is no more than one arc connecting any pair of vertices.
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Trail
A walk in which no arc is repeated
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Tree
A simple connected graph with no cycles.
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Walk
A sequence of arcs in which the end of each arc (except the last) is the beginning of the next
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## Other cards in this set

### Card 2

#### Front

Vertices fall into two sets and each edge has a vertex with one set at one end and the other set at the other end.

Bipartite Graph

### Card 3

#### Front

simple graph in which every pair of vertices is connected by an edge.

### Card 4

#### Front

Where a path exists between every pair of vertices.

A closed path