What is the Hamiltonian path in a graph?

What is the Hamiltonian path in a graph?

A Hamiltonian path in a graph is a path that visits each vertex exactly once, except for the starting and ending vertices, which are the same. In other words, it is a path that traverses through all the vertices of the graph without repeating any vertex, forming a cycle. This concept is named after Sir William Rowan Hamilton, an Irish mathematician who first studied such paths. Hamiltonian paths are important in graph theory as they provide a way to explore the connectivity and structure of a graph.