# D1 Edexcel Definitions

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• Created by: jasmine
• Created on: 26-05-16 12:16
Graph
A graph consists of vertices (nodes) which are connected by edges (arcs)
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Subgraph
A subgraph is a part of a graph
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Weighted Graph
A graph in which there is a number associated with each edge (its weight)
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Degree of valency/order
The number of edges incident to a vertex
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Path
A finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex of the next and in which no vertex appears more than once
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Walk
A path in which you are permitted to return to vertices more than once
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Cycle/ Circuit
A closed path i.e. the end vertex of the last edge is the start vertex of the first edge
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Loop
An edge that starts and finishes at the same vertex
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Simple Graph
A graph in which there are no loops and not more than one edge connecting any pair of vertices
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Digraph/ Directed Edges
A graph in which the edges have a direction associated with them- the edges are known as directed edges
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Tree
A connected graph with no cycles
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Spanning Tree
A subgraph of a graph which includes al 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 its arcs is as small as possible
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Bipartite Graph
A graph conisisting of two sets of vertices, X and Y. The edges only join vertices in X to vertices in Y, not vertices within a set
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Complete Graph
A graph in which every vertex is directly connected by an edge to each of the other vertices. If the graph has n vertices, the connected graph is denoted Kn
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Complete Bipartite Graph
A graph iin which there are r vertices in set X and s vertices in set Y (denoted Kr,s)
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Isomorphic Graphs
A graph showing the same information as another but which is drawn differently
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A matrix which records the number of direct links between vertices
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Distance Matrix
A matrix which records the weights on the edges. Where there is no weight, this is indicated by '-'.
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Eulerian Graph
All valencies are even. Graph is traversable
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Semi-Eulerian Graph
If precisely two vertices are odd and the rest even, the graph is semi-traversable
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Early event time
The earliest time of arrival at the event allowing for the completion of all preceeding acctivities.
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Late event time
The latest time that the event can be left without extending the time needed for the project.
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Critical Activity
An activity where any increase in its duration results in a corresponding increase in the duration of the whole project i.e. float of 0
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Critical Path
A path from the source node to the sink node which entirely follows critical activities. It is the longest path contained in the network
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Total Float
The amount of time an activity may be delayed without affecting the duration of the project
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Matching
A matching is a 1 to 1 pairing of some, or all, of the elements of one set, X, with elements of a second set, Y, in a bipartite graph
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Maximal Matching
A matching in which the number of arcs is as large as possible
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Complete Matching
A complete matching is the 1 to 1 pairing of all of the elements of one set, X, with elements of a second set, Y, in a bipartite graph
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Alternating Path
A path starting at an unmatched node on one side of the bipartite graph and finishes at an unmatched node on the other side. It uses arcs that are alternated 'not in' or 'in' the initial matching
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## Other cards in this set

### Card 2

#### Front

A subgraph is a part of a graph

Subgraph

### Card 3

#### Front

A graph in which there is a number associated with each edge (its weight)

### Card 4

#### Front

The number of edges incident to a vertex

### Card 5

#### Front

A finite sequence of edges, such that the end vertex of one edge in the sequence is the start vertex of the next and in which no vertex appears more than once

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