Maths Apps Graphs and Networks - Flashcards

Vertices

Points of a graph

Edges

Lines of a graph

Graph

A diagram that consists of a set of vertices (points) that are connected by a set of edges (lines)

Adjaecent Vertices

Two vertices that are connected by one or more edges

Multiple Edges

When two or more edges connect to the same pair of vertices

Loop

An edge that connects a vertex to itself

Isolated Vertex

A vertex that is not connected to any other vertex

The Degree

Refers to the number of edges connected to that vertex

The degree sum, S, formula

S = 2 x number of edges

Subgraph

A graph that is part of another graph, such that it contains no new edges or vertices

Network

A group of interconnected elements (people, places, teams) for which a graph can be used to show these connections

Simple Graph

Contains no loops, or multiple edges

Complete Graph

A simple graph where every vertex is connected to every other vertex

Edges formula

n(n-1)/2

Bridge

A single edge which keeps the graph connected

Bipartite Graph

A graph whose vertices can be split into two distinct groups so that each edge connects each vertex in the first group to a vertex in a second group

Planar Graph

A graph that has no edges that cross

Faces

The regions of a planar graph that are enclosed or bounded by edges

Euler’s Formula

v + f - e = 2