In the mathematical field of graph theory, the complement or inverse of a graph G is a graph H on the same vertices such that two distinct vertices of H are adjacent if and only if they are not adjacent in G. That is, to generate the complement of a graph, one fills in all the missing edges required to form a complete graph, and removes all the edges that were previously there. The complement is not the set complement of the graph; only the edges are complemented. (Wikipedia).
Graph Theory: 48. Complement of a Graph
In this video I define the complement of a graph and what makes a graph self-complementary. I show some examples, for orders 4 and 5 and discuss a necessary condition on the order of a graph for it to be self-complementary. Finally I give a brief description of a constructive algorithm f
From playlist Graph Theory part-8
What is the Complement of a Graph? | Graph Theory, Graph Complements, Self Complementary Graphs
What is the complement of a graph? What are self complementary graphs? We'll be answering these questions in today's video graph theory lesson! If G is a graph, the complement of G has the same vertex set but the "opposite" edge set. That means two vertices are adjacent in G Complement if
From playlist Graph Theory
Minimum and Maximum Degree Vertices in Complement Graphs | Graph Complements, Graph Theory
How do we know what vertices will have the minimum and maximum degree of a complement graph based on the degrees of the original graph? We go over properties about just this topic in today's video graph theory lesson! Let G be a graph with vertices v and u such that the degree of v is the
From playlist Graph Theory
Proof: A Graph or its Complement Must be Connected | Graph Theory, Graph Complements
A graph and its complement cannot both be disconnected. Why is this? We'll find out in today's video graph theory lesson, where we prove that at least one of a graph or its complement has to be connected! The proof is fairly straightforward, we begin with a disconnected graph G and want
From playlist Graph Theory
Reducing to Clique - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
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
Complement of Independent Set is Vertex Cover | Graph Theory
We prove the complement of an independent vertex set is a vertex cover. This makes for an easy direct proof once we recall our definitions. An independent vertex set is a set of vertices, no two of which are adjacent. A vertex cover is a set of vertices such that every edge has at least on
From playlist Graph Theory
Maths for Programmers: Sets (Complement & Involution Laws)
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From playlist Maths for Programmers
Proof: A Graph or its Complement is not Bipartite | Graph Theory, Bipartite Graphs
If G is a graph with at least 5 vertices, at most one of G or G complement is bipartite. We will prove this graph theory result directly using the well know bipartite graph theorem relating to odd cycles. The only way the statement is false is if there exists a graph G of order 5 or more
From playlist Graph Theory
Proof: Complement of Regular Non-Eulerian Graph is Eulerian | Graph Theory, Euler Graphs
If the complement of a connected, regular, non-Eulerian graph is also connected, then it is Eulerian! We will prove this result in today's graph theory lesson using some argument about the degree sums of different graphs, and whether they're even or odd! Proof connected graph is Eulerian
From playlist Graph Theory
Proof: Cut Vertex is not a Cut Vertex of the Complement Graph | Graph Theory
Let v be a cut vertex of a graph G. Then v is not a cut vertex of G complement. We prove this result in today's video graph theory lesson! Lesson on cut vertices: https://www.youtube.com/watch?v=D1nYRgXPRyM Lesson on complement graphs: https://www.youtube.com/watch?v=1HNVZ6nNw8w I hope
From playlist Graph Theory
Double Complement of a Set | Set Theory
What is the complement of the complement of a set? In today's set theory lesson we'll discuss double complements with respect to "absolute complements - being complements taken with respect to a universal set as opposed to relative complements. When we consider a universal set, every oth
From playlist Set Theory
Bound on the Sum of Minimum Degrees of Graphs and their Complements | Graph Theory Proofs
We know the degree of a vertex in a simple graph with n vertices has an upper bound of n-1. The degree of a vertex is n-1 when it is adjacent to every vertex in the graph except for itself (it cannot be adjacent to itself). Then certainly the minimum degree of a graph is less than or equal
From playlist Graph Theory
Complement of Vertex Cover is Independent Vertex Set | Graph Theory
We prove the complement of a vertex cover is an independent vertex set. Recall a vertex cover is a set of vertices covering all edges of the graph, meaning every edge has at least one end vertex in the cover. As a result, the complement of a cover cannot possible have two vertices joined b
From playlist Graph Theory
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Use a Venn diagram to Determine Cardinality of Sets (Level 2)
This video defines cardinality and then determines the number of elements in sets based upon a Venn diagram. It includes union, intersection, and complements of sets. http://mathispower4u.com
From playlist Sets