# A Perspective on the Early History of Grahp Theory

**Specialeforsvar** ved Lise Rathmann Sønderby Jensen

**Titel:** A Perspective on the Early History of Graph Theory

**Abstract: **The history of graph theory has only been explored by a few scientists. I found, no one had written about how it became a mathematical discipline. Therefore, this thesis is about how graph theory became its own mathematical discipline. The foundation for the thesis is the following problem statement:

It is the aim of this thesis to investigate the development of graph theory into a mathematical discipline by analyzing the first works which gathered the material on graph theory existing at their time. The focus will be on giving an assessment of the driving forces behind the development, in particular the role of pure mathematical ideas and problems found outside of mathematics as driving forces in the history of graph theory.

An account of the early history of graph theory serves as an introduction to graph theory and its history. The main part of the thesis consists of an analysis of four of the first works which gathered the material on graph theory in one work. I chose to study the four sources:

- Francois Édouard Anatole Lucas'(1842-1891)
*Récréations Mathématiques*(1891-1894). - Max Dehn(1878-1952) and Poul Heegaard's(1878-1948)
*Analysis Situs*(1907). - André Sainte-Lagué's(1882-1950)
*Les Reseaux (ou graphes)*(1926). - The English translation of Dénés König's(1884-1994) book
*Theorie der endlichen und unendlichen Graphen*from (1936).

These sources were chosen because of their differences in genre, content, purpose, and in publication date. They are meant to show different steps in the development of graph theory into a discipline.

To give an assessment of the driving forces behind graph theory becoming its own mathematical discipline, the four works have been compared.

I found, the most important driving force in graph theory becoming its own mathematical discipline was the people who could see the value of graph theory, when others could not. What drove these people were different things; for many of them, it was pure mathematics, but to some, it was problems in the physical world or other sciences which lead them to study graph theory. Recreational mathematics played an important role in the very early development of graph theory, and it kept being associatedwith graph theory for a long time. Furthermore, applications of graph theory to other sciences, other mathematical disciplines, the physical world, etc., were important in the discipline that it became as presented by Dénés König.

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**Vejleder:** Jesper Lützen**Censor: ** Ivan Tafteberg Jacobsen