Constraint programming | Extensions and generalizations of graphs
An ordered graph is a graph with a total order over its nodes. In an ordered graph, the parents of a node are the nodes that are adjacent to it and precede it in the ordering. More precisely, is a parent of in the ordered graph if and . The width of a node is the number of its parents, and the width of an ordered graph is the maximal width of its nodes. The induced graph of an ordered graph is obtained by adding some edges to an ordering graph, using the method outlined below. The induced width of an ordered graph is the width of its induced graph. Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its parents are not joined by an edge, that edge is added. In other words, when considering node , if both and are parents of it and are not joined by an edge, the edge is added to the graph. Since the parents of a node are always connected with each other, the induced graph is always chordal. As an example, the induced graph of an ordered graph is calculated. The ordering is represented by the position of its nodes in the figures: a is the last node and d is the first. Node is considered first. Its parents are and , as they are both joined to and both precede in the ordering. Since they are not joined by an edge, one is added. Node is considered second. While this node only has as a parent in the original graph, it also has as a parent in the partially built induced graph. Indeed, is joined to and also precede in the ordering. As a result, an edge joining and is added. Considering does not produce any change, as this node has no parents. Processing nodes in order matters, as the introduced edges may create new parents, which are then relevant to the introduction of new edges. The following example shows that a different ordering produces a different induced graph of the same original graph. The ordering is the same as above but and are swapped. As in the previous case, both and are parents of . Therefore, an edge between them is added. According to the new order, the second node that is considered is . This node has only one parent. Therefore, no new edge is added. The third considered node is . Its only parent is . Indeed, and are not joined this time. As a result, no new edge is introduced. Since has no parent as well, the final induced graph is the one above. This induced graph differs from the one produced by the previous ordering. (Wikipedia).
This video explains the definitions of simple graphs, multigraphs, connected and not connected graphs, complete graphs, and the Handshake lemma. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Order and Size of a Graph | Graph Theory
What is the order and size of a graph? We'll go over them both in this math lesson! A graph is an ordered pair with a vertex set and an edge set. The order of a graph is the cardinality of its vertex set, which is the number of vertices in the graph. The size of a graph is the cardinality
From playlist Graph Theory
Determine If an Ordered Pair is a Solution to a Linear Equation
This video explains how to determine if an ordered pair is a solution to a given linear equation. http://mathispower4u.com
From playlist Graphing Linear Equations Using a Table of Values
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
This video answers two questions: What are ordered pairs? How do you graph them?
From playlist Algebra
Use a Graph Determine Ordered Pair Solutions of a Linear Inequality in Two Variable
This video explains how to select ordered pair solutions from the graph of a linear inequality of two variables. mathispower4u.com
From playlist Solving Linear Inequalities in Two Variables
Graph Neural Networks, Session 2: Graph Definition
Types of Graphs Common data structures for storing graphs
From playlist Graph Neural Networks (Hands-on)
Underlying Graphs of Digraphs | Directed Graphs, Graph Theory
What are underlying graphs of directed graphs in graph theory? This is a sort of undirected graph that "underlies" or "lies under" a directed graph. But how is it actually defined? We'll go over that in today's video graph theory lesson! A simple way to define the underlying graph of a di
From playlist Graph Theory
From playlist Algorithms 1
Extremal theory of ordered graphs – Gábor Tardos – ICM2018
Combinatorics Invited Lecture 13.3 Extremal theory of ordered graphs Gábor Tardos Abstract: We call simple graphs with a linear order on the vertices ‘ordered graphs’. Turán-type extremal graph theory naturally extends to ordered graphs. This is a survey on the ongoing research in the ex
From playlist Combinatorics
Nicole Schweikardt: Databases and descriptive complexity – lecture 2
Recording during the meeting "Spring school on Theoretical Computer Science (EPIT) - Databases, Logic and Automata " the April 11, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by wor
From playlist Numerical Analysis and Scientific Computing
The abstract chromatic number - Leonardo Nagami Coregliano
Computer Science/Discrete Mathematics Seminar I Topic: The abstract chromatic number Speaker: Leonardo Nagami Coregliano Affiliation: University of Chicago Date: March 22, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Topological Sort | Kahn's Algorithm | Graph Theory
Source code repository: https://github.com/williamfiset/algorithms#graph-theory Video slides: https://github.com/williamfiset/algorithms/tree/master/slides Website: http://www.williamfiset.com Audio intro/outro composed by Richard Saney (rnsaney@gmail.com) 0:00 Intro 0:22 Topological s
From playlist Graph Theory Playlist
Proof: Connected Graph of Order n Has at least n-1 Edges | Graph Theory
A connected graph of order n has at least n-1 edges, in other words - tree graphs are the minimally connected graphs. We'll be proving this result in today's graph theory lesson! We'll be using a special type of contradiction proof called a proof by minimum counterexample. If we assume t
From playlist Graph Theory
Research Working Session: Tuesday, August 2, 2022 [Multicomputation]
This a research session on Multicomputation. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram here: https://www.twitch.tv/stephen_wolfram/ Follow us on our officia
From playlist Science and Research Livestreams
Graph Theory: 46. Relation Between Minimun Degree and Subtrees
It is not surprising that a tree of order k is a subgraph of a complete graph of order at least k. Here I'll explain the result that shows for every tree T of order k, any graph with minimum degree at least k-1 will contain a subgraph isomorphic to T. The proof is by induction on the ord
From playlist Graph Theory part-8
Random orderings and unique ergodicity of automorphism groups - Russell Lyons
Conference on Graphs and Analysis Russell Lyons June 4, 2012 More videos on http://video.ias.edu
From playlist Mathematics
C# Trees and Graphs Explained | Data Structures and Algorithms in C# | C# Tutorial | Simplilearn
🔥Post Graduate Program In Full Stack Web Development: https://www.simplilearn.com/pgp-full-stack-web-development-certification-training-course?utm_campaign=CSharpTreesAndGraphsExplained-IqQ7QpmiBJ0&utm_medium=DescriptionFF&utm_source=youtube 🔥Caltech Coding Bootcamp (US Only): https://www.
From playlist C# Training 🔥[2022 Updated]
Ex: Determine If An Ordered Pair is a Solution to a Linear Equation
This video explains how to determine in a given ordered pair is a solution to a linear equation. http://mathispower4u.com
From playlist Graphing Linear Equations Using a Table of Values
A glimpse of continuous combinatorics via natural quasirandomness - Leonardo Coregliano
Short Talks by Postdoctoral Members Topic: A glimpse of continuous combinatorics via natural quasirandomness Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: September 23, 2021
From playlist Mathematics