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CYCLE OF EULER

A Eulerian cycle is one way that runs through all vertices (nodes) of a graph from one and only once for each arc (edge) of the graph, being a necessary condition to return to the initial vertex output (cycle = path in a graph where vertex match departure and initial or final vertex or goal). A formal definition defines it as "one cycle containing all edges of a graph only once."

In the picture, c = {1,2,3,4,6,3,5,4,1} is an Eulerian cycle, then a graph is Eulerian.

A graph is a representation, a model consisting of a number of vertices (nodes) and a number of arcs (edges) that relate to each edge or arc has the ability to connect two nodes. The word cycle is used in graph theory to indicate a closed path in a graph, ie the starting node and end node are the same, as a counterpart a Hamiltonian path is a path through all vertices of a graph without passing twice on the same vertex. If the road is closed call a Hamiltonian cycle.

If a graph admits an Eulerian cycle, Eulerian graph is called. Determines

Euler cycle in the following figure:

Why is it useful?

in everyday life we \u200b\u200buse very often when we visit all our friends and ultimately return home or when we are in a museum, we visit all the rooms and back out through the same entrance. is more than anything to analyze all the way and see if there is an error and improvement.