Further Maths- Graphs and networks

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21 Terms

1

Graph

A set of points that are connected by lines

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2

Node

A vertex

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3

Weighted graph

If there is a number associated with an edge

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4

Valency

Order

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5

Order

The number of arcs incident from a node

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6

Walk

A route through the graph from one edge to the next

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7

Path

Is a walk in which no vertex is visited more than once

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8

Trail

Is a walk in which no edge is visited more than once

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9

Cycle

Is a walk where the end vertex and start vertex are the same

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10

Hamiliton Cycle

Is a cycle that includes every vertex

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11

Loop

An edge that starts and finished at the same node

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12

Simple Graph

Has no loops and each vertex is connected to another vertex only once

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13

Connected graph

If all the vertices are connected

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14

Digraph

A graph that has direction associated to it

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15

Euler's handshaking lemma

In any undirected graph, the sum of the degrees of the vertices is equal to 2x the number of edges.

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16

Tree

A connected graph with no cycles

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17

Spanning Tree

a subgraph which includes all the vertices and is also a tree

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18

Isomorphic

Two graphs showing the same information but drawn differently

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19

completed graph

Is a graph where each vertex is connected to each of the other vertices by a single edge

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20

Kn

A completed graph with n vertices

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21

Degree

Order

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