Euler’s And Hamilton’s Path Through One-Dimension Space

This article will present a technique for traversing a graph. Several questions arise here. For example, can we walk along the edges of a graph starting from a vertex and returning to it by visiting each edge of the graph exactly once? Similarly, can we walk along the edges of a graph starting from a vertex and returning to it while visiting each vertex of the graph exactly once? As can be seen, both questions are identical, but what is important is to consider two circuits that answer the above questions, namely the Euler circuit and the Hamilton circuit. Solving the Hamilton circuit for most graphs is very difficult. In this section, we will examine these questions and discuss the difficulty of solving them.