5 Questions
In graph theory, what are the objects that correspond to mathematical abstractions called?
Vertices (also called nodes or points)
What is the term for the related pairs of vertices in a graph?
Edge (also called link or line)
How are graphs typically depicted in diagrammatic form?
As a set of dots or circles for the vertices, joined by lines or curves for the edges.
What is the difference between directed and undirected graphs, using the example of people at a party?
In an undirected graph, if there is an edge between two people, it means they both shake hands. In a directed graph, an edge from person A to person B means that A owes money to B, without the necessity of reciprocation.
Who first used the word 'graph' in the context of graph theory and when?
J. J. Sylvester in 1878
Study Notes
Graph Theory Basics
- In graph theory, mathematical abstractions are represented by vertices (also called nodes) and edges.
Graph Components
- Related pairs of vertices in a graph are called adjacent vertices.
Graph Representations
- Graphs are typically depicted in diagrammatic form using points (vertices) and lines or curves (edges) that connect them.
Directed vs Undirected Graphs
- Directed graphs have edges with direction (e.g., one person at a party admires another, but not necessarily vice versa).
- Undirected graphs have edges without direction (e.g., two people at a party are friends, and the relationship is mutual).
Graph Theory History
- The term 'graph' was first used in the context of graph theory by Leonhard Euler in the 18th century.
Test your knowledge of graph theory with this quiz on graph structures, vertices, and edges. See how well you understand the fundamental concepts of discrete mathematics and graph theory.
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