Fundamentals of Graph Theory

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Course Outline

  1. Graph definition and components
  2. Graph vocabulary and types
  3. Graph properties and characteristics
  4. Degree and order of graphs
  5. Types of graphs and applications

1. Graph definition and components

Key Concepts & Definitions

  • Graph: An set composed of two parts: a set of points called vertices and a set of segments called edges connecting some pairs of vertices (G = (S, A)).
  • Vertices (or nodes): Points in a graph representing entities. They are the fundamental units of the graph.
  • Edges (or links): Segments that connect pairs of vertices, representing relationships or connections between entities.

Essential Points

  • A graph is characterized by its vertices and edges.
  • The set of vertices is often denoted as S = {S1, S2, S3, ..., Sn}.
  • The set of edges is often denoted as A = {A1, A2, A3, ..., An}.
  • The number of vertices is called the cardinality of S (denoted as s).
  • The number of edges is called the cardinality of A (denoted as n).
  • A graph can be represented as G = (s, n), where s is the number of vertices and n is the number of edges.

Key Takeaway

A graph is a structure composed of points called vertices and segments called edges that connect some pairs of these vertices, serving as a fundamental model for representing relationships between entities.

2. Graph vocabulary and types

Key Concepts & Definitions

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Aperçu du QCM

1. When was the fundamental concept of a graph, including its components like vertices and edges, first established in mathematical literature?

2. Who is credited with first establishing the fundamental concepts of graph theory, including vertices and edges, and in which year?

3. What is the primary role of directed graphs in modeling real-world systems?

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Aperçu des flashcards

Graph — components?

Vertices and edges

Graph — components?

Vertices and edges.

Graph vocabulary — types?

Simple, complete, directed, connected, stable

Loop — definition?

Edge connecting a vertex to itself.

Complete graph — property?

Every pair of vertices connected.

Directed graph — role?

Edges have direction arrows.

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Que contient la fiche de révision sur Fundamentals of Graph Theory ?

La fiche de révision couvre les notions essentielles de Fundamentals of Graph Theory. Elle est structurée par thématiques pour faciliter l'apprentissage et la mémorisation, avec des définitions clés, des explications et des synthèses.

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