Euler Circuit Of A Graph Essay

1. The definition of a graph is a limited set of points called vertices which are connected by line segments called edges. A graph is illustrated in a diagrammatic form as a set of dots. These dots are the vertices which are joined by lines or even curves that make up the edges. The definition of a path can be a limited or unlimited sequence of edges which connects a sequence of vertices in a graph. The connected sequence of edges starts at one vertex and ends at another, it can be the same but doesn’t always have to be. the definition of a circuit is a path that must start and end at the same vertex. The starting point of a circuit is called the reference point. (128)

2. An Euler path is a path that will cross through each edge of a graph exactly once. An Euler path can start at any point and end with a different end point. A graph that has an Euler path can have either zero or two odd vertices, however the rest must be even. An Euler circuit is a circuit that goes through every edge of the graph exactly once. The difference between the two is that an Euler circuit must always start and end at the same vertex, whereas a path does not. Every graph has a path, however not every graph will have a path and a circuit. For a graph to have an Euler circuit each vertices have

The definition of a Hamilton path is a path that contains each vertex of a graph exactly once. Figuring out if a graph has a Hamilton path is actually quite difficult and for a graph to have a Hamilton path they would need to have endpoints that are adjacent. If a graph does have a Hamilton path it is then called a traceable graph. The way to find an existing Hamilton path in a graph you would have to use Np-complete. The Hamilton path is named after William Rowan Hamilton, who created the Hamilton puzzle as a means to find a Hamiltonian cycle in a graph. A Hamilton circuit is a path that begins and ends at the same vertex and passes through all other vertices of the graph exactly one time.