Complete graph

What is a Complete Graph? | Graph Theory

What is a complete graph? That is the subject of today's lesson! A complete graph can be thought of as a graph that has an edge everywhere there can be an edge. This means that a graph is complete if and only if every pair of distinct vertices in the graph is joined by an edge. So if, in a

From playlist Graph Theory

AQA Decision 1 3.03 Complete Graphs Kn

I introduce the concept of a complete graph and find how many edges there would be for a complete graph with n vertices.

From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)

What are Complete Bipartite Graphs? | Graph Theory, Bipartite Graphs

What are complete bipartite graphs? We'll define complete bipartite graphs and show some examples and non-examples in today's video graph theory lesson! Remember a graph G = (V, E) is bipartite if the vertex set V can be partitioned into two sets V1 and V2 (called partite sets) such that

From playlist Graph Theory

Graph Theory FAQs: 01. More General Graph Definition

In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o

From playlist Graph Theory FAQs

Graph Theory: Number of Routes and Circuits of a Complete Graph

This lesson explains how to find the total number of routes and circuits of complete graphs. Site: http://mathispower4u.com

From playlist Graph Theory

Lecture 1 Graphs Definition

A formal definition of a Graph and its properties

From playlist Graph Theory

Graph Theory: 05. Connected and Regular Graphs

We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to

From playlist Graph Theory part-1

What are Connected Graphs? | Graph Theory

What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr

From playlist Graph Theory

A Few Conceptual Examples with Statistical Graphs

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A Few Conceptual Examples with Statistical Graphs

From playlist Statistics

Chromatic Number of Complete Graphs | Graph Theory

What are the chromatic numbers of complete graphs on n vertices? As we’ll see in today’s graph theory lesson on vertex coloring, we need exactly n colors to properly color the complete graph K_n. Intro to Graph Colorings: https://youtu.be/3VeQhNF5-rE Recall that a proper coloring (or ju

From playlist Graph Theory

Bipartite Graphs with Isolated Vertices | Graph Theory, Complete Bipartite Graphs

We know what a bipartite graph is, and we know about complete bipartite graphs. But how do these definitions work with isolated vertices that have no neighbors? We'll go over just that in today's graph theory lesson! Remember that a bipartite graph is a graph whose vertices that can be pa

From playlist Graph Theory

Which Complete Graphs are Planar? | Graph Theory

Which complete graphs are planar? Which complete graphs are nonplanar? We'll answer this question in today's graph theory lesson! We'll see that K1, K2, K3, and K4 are all planar complete graphs. Then, we'll prove that K5 is nonplanar and see why that implies no complete graph with at le

From playlist Graph Theory

Vertex Connectivity of a Graph | Connectivity, K-connected Graphs, Graph Theory

What is vertex connectivity in graph theory? We'll be going over the definition of connectivity and some examples and related concepts in today's video graph theory lesson! The vertex connectivity of a graph is the minimum number of vertices you can delete to disconnect the graph or make

From playlist Graph Theory

Number of Edges in a Complete Graph (Using Combinations) | Graph Theory, Combinatorics

How many edges are in a complete graph? This is also called the size of a complete graph. We'll be answering this question in today's video graph theory lesson, the first lesson on a whiteboard! Remember that a complete graph K_n is a graph with n vertices and edges joining every pair of

From playlist Graph Theory

Vertex Cuts in Graphs (and a bit on Connectivity) | Graph Theory, Vertex-Connectivity

What is a vertex cut of a graph? And how can we use vertex cuts to describe how connected a graph is? We have discussed cut vertices and connected graphs before, but by tying them together in a way, we are able to characterize different levels of connectivity in graphs. The focus of this l

From playlist Graph Theory

Vertex Covering Number of Complete Graphs | Graph Theory Exercises

We discuss and prove the vertex covering number of a complete graph Kn is n-1. That is, the minimum number of vertices needed to cover a complete graph is one less than its number of vertices. This is because, put simply, if we are missing at least 2 vertices in our attempted vertex cover,

From playlist Graph Theory Exercises

Matchings, Perfect Matchings, Maximum Matchings, and More! | Independent Edge Sets, Graph Theory

What are matchings, perfect matchings, complete matchings, maximal matchings, maximum matchings, and independent edge sets in graph theory? We'll be answering that great number of questions in today's graph theory video lesson! A matching in a graph is a set of edges with no common end-ve

From playlist Graph Theory

How Many Graphs on n Vertices? | Graph Theory

We count the number of simple graphs there are on n vertices. We are counting labeled graphs, so we're answering the question of how many graphs there are with vertex set {1, 2, 3, ..., n}. This requires we know how many edges are possible on n vertices, and then the result is straightforw

From playlist Graph Theory