Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to model pairwise relations between objects. The history of graph theory is quite fascinating, with roots that can be traced back to the 18th century.

Early Developments

  • 1736: Euler's work on the bridges of Königsberg laid the foundation for graph theory.
  • 1857: Augustus De Morgan introduced the term "graph" in his book "On the Mathematical Theory of Networks and Graphs."

Key Milestones

  • 1878: James Joseph Sylvester coined the term "graph" in a paper titled "On a New System of Graphical Representations."
  • 1936: Kazimierz Kuratowski provided a necessary and sufficient condition for a graph to be planar.
  • 1957: The concept of the adjacency matrix was introduced by Frank Harary.

Famous Graphs

  • Kuratowski's Five-Vertex Graph: A minimal non-planar graph.
  • Complete Graph: A graph in which every pair of vertices is connected by an edge.
  • Cayley's Tree: A graph representing the edges of a tree with (n) labeled nodes.

Kuratowski's Five-Vertex Graph

Applications

Graph theory has applications in various fields, including computer science, physics, and social sciences.

  • Computer Science: Graphs are used to model algorithms, data structures, and networks.
  • Physics: Graphs are used to model the structure of materials and the flow of electricity.
  • Social Sciences: Graphs are used to model social networks and the spread of information.

For more information on graph theory, you can visit our tutorials page.

The history of graph theory is a testament to the power of mathematics in solving real-world problems. As we continue to explore the field, we can expect to see even more fascinating developments.