In the history of mathematics, Euler's solution of the Königsberg bridge problem is considered to be the first theorem of graph theory and the first true proof in the network theory, [4] a subject now generally …

The Four-Color Problem was the first major mathematical theorem whose proof depended in part on modern computers. Each of these problems, although trivial on the surface, has led to incredible …

At first, the usefulness of Euler’s ideas and of “graph theory” itself was found only in solving puzzles and in analyzing games and other recreations. In the mid 1800s, however, people began to realize that …

Nov 13, 2025 · The history of graph theory may be specifically traced to 1735, when the Swiss mathematician Leonhard Euler solved the Königsberg bridge problem.

This theorem gets its name from the fact that it is often the first theorem encountered when one is learning graph theory.

In any graph, the number of vertices of odd degree must be even. This is a consequence of the equation given above: if a sum (sum of vertex degrees, left side of the equation) is even, there must be an …

The minimum degree and maximum degree of a vertex in the graph G are denoted by δ(G) and Δ(G) , respectively. A graph in which each vertex has degree r is called an r-regular graph (or simply …

In a graph G, the set of all neighbors of a vertex x is denoted NG(x). And when the graph G is fixed in the discussion, this is typically abbreviated to just N(x).

In 1736, Euler tackled the famous problem known as the Seven Bridges of Königsberg, where he introduced the concept of a graph and developed the fundamental theorem of graph theory. His …

Our first theorem of graph theory connects the sum of the degrees to the number of edges and is usually called the Handshaking lemma, as it can be interpreted as stating that the sum of the number of …