Eulerian cycle

An Eulerian cycle is a path within a graph that traverses each edge exactly once and returns to the starting vertex. This concept originated from the famous Königsberg bridge problem, where mathematician Leonhard Euler determined it was impossible to cross all seven bridges of the city exactly once.123

In graph theory, a graph consists of vertices (points) connected by edges (lines). For an Eulerian cycle to exist in a connected graph, all vertices must have an even degree, meaning an even number of edges connect to each vertex. If a graph has exactly two vertices with an odd degree, an Eulerian path (which doesn't necessarily end at the starting vertex) is possible. The study of these concepts is fundamental to graph theory, a branch of mathematics with applications in various fields.12