Writers:

1**. MUHAMMAD PARIS AL-FAJRI**

**2. BUNGA**

**3. MAURISKA KHAIRUNNISA**

**4. ANGGUN SHALSABILLA**

*(Department Mathematics and Data Science, Andalas University)*

Leonhard Euler (1707-1783) was one of the greatest mathematicians in history, who made many important contributions to the field of mathematics. One of his most famous contributions was the solution to the Königsberg bridge problem.

The Königsberg bridge problem is one of the classic problems in the history of mathematics related to graph theory. The city of Königsberg, now called Kaliningrad, was located between two sides of the Pregel river and had two islands connected by seven bridges. The townspeople often took walks around the river and wondered if there was a way to cross each bridge exactly once without having to return to the starting point.

This problem caught the attention of Leonhard Euler, a Swiss mathematician who lived in the 18th century. Euler was one of the most prolific and influential mathematicians in history, who made major contributions to various fields of mathematics, such as calculus, analysis, algebra, number theory, geometry, mechanics, and astronomy. Euler is also known as the father of graph theory, as he was the first to formulate and prove basic theorems about graphs.

Euler solved the Königsberg bridge problem in a brilliant and innovative way. He realized that it doesn’t matter how long the bridge is or the shape of the island, what matters is the relationship between the bridge and the island. He then described the city of Königsberg as a graph, which is a mathematical structure consisting of vertices and edges. The vertices represented the island, and the edges represented the bridge, so the problem of the Königsberg bridge could be simplified.

Euler then posed the question, “when can a graph be traversed by crossing every edge exactly once?”, and he found the answer by using the concept of vertex degree, which is the number of edges associated with a vertex. Euler proved that a graph is traversable in this way if and only if it is connected and has zero or two vertices of odd degree. The Königsberg graph does not fulfill this condition, as it has four vertices of odd degree. Therefore, Euler concluded that there was no way to solve the Königsberg bridge problem.

Euler’s proof is one of the most elegant and important mathematical proofs in history. He not only solved an entertaining puzzle, but also created a new branch of mathematics, graph theory. Graph theory now has many applications in various fields, such as computer science, biology, sociology, cryptography, and optimization. Euler has opened the door to new discoveries and shown the beauty and wonder of mathematics.

BIBLIOGRAPHY

Hartsfield, Nora (1990), Pearls in Graph Theory A comprehensive introduction, pp, 49-55.

Wilson J Robin, (1976), Graph Theory, pp, 64-65, 204.

Chartrand, Gary, (2005), Introduction to Graph Theory, pp, 133-138.***

See Shields, Rob (Desember 2012). ‘Cultural Topology: The Seven Bridges of Königsburg 1736’ in Theory Culture and Society 29. pp.43-57