Decision Maths Chapter 2 Definitions Flashcards Preview

Further Maths A Level Edexcel > Decision Maths Chapter 2 Definitions > Flashcards

Flashcards in Decision Maths Chapter 2 Definitions Deck (20)
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1

Graph

A group of points (called vertices or nodes) that are connected by lines (Edges or Arcs).

2

Weighted Graph

A graph that has a number associated with each edge.

3

Subgraph

A graph each of whose vertices belongs to G and each of whose edges belongs to G. It is simply a part of the original graph.

4

Degree/Valency/Order of a vertex

The number of edges incident to it.

5

Walk

A route through a graph along edges from one vertex to the next.

6

Path

A walk, in which no vertex is visited more than once.

7

Trail

A walk in which no edges are visited more than once.

8

Cycle

A walk, in which the end vertex is the same as the start vertex and no other vertex is visited more than once.

9

Hamiltonian Cycle

A cycle that includes every vertex.

10

Connected Graph

A graph where all vertices are connected.

11

Loop

An edge that starts and finishes at the same vertex.

12

Simple Graph

A graph in which there are no loops and there is at most one edge connecting any pair of vertices.

13

Directed Graph

If the edges of a graph have an associated direction.

14

Euler's Handshake Lemma

The sum of the degrees of the vertices is equal to 2 x the number of edges.

15

Tree

A graph with no cycles

16

Spanning Tree

A subgraph that involves all of the vertices and is also the tree.

17

Complete Graph

A graph in which every vertex is directly connected by a single edge to each of the other vertices.

18

Isomorphic Graph

Graphs that show the same information but may be drawn differently.

19

Adjacency Matrix

A matrix where each entry describes the number of arcs joining the corresponding vertices.

20

Distance Matrix

A matrix where each entry describes the weight of each arc.