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An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once. If such a cycle exists, the graph is called Eulerian or unicursal. [4] The term "Eulerian graph" is also sometimes used in a weaker sense to denote a graph where every vertex has even degree.
Euler's argument shows that a necessary condition for the walk of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree. This condition turns out also to be sufficient—a result stated by Euler and later proved by Carl Hierholzer. Such a walk is now called an Eulerian trail or Euler walk in his honor ...
The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. [ 1 ] [ 2 ] This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.
An Eulerian circuit (also called an Eulerian cycle or an Euler tour) is a closed walk that uses every edge exactly once. An Eulerian graph is a graph that has an Eulerian circuit. For an undirected graph, this means that the graph is connected and every vertex has even degree.
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
In Google Scholar, "Euler graph" is used about 1/4 as often as "Eulerian graph", and without noticeably different meaning (except that it is also used for other things: the multigraphs of crossings and arcs of Euler diagrams, and something algebraic related to Eulerian numbers; don't ask me why Euler graphs go with Eulerian numbers and not ...
Living longer doesn’t always mean living healthier. That’s according to a study published in JAMA Network Open, which found a "widening gap between lifespan and healthspan" among 183 countries.
An Eulerian circuit is a directed closed trail that visits each edge exactly once. In 1736, Euler showed that G has an Eulerian circuit if and only if G is connected and the indegree is equal to outdegree at every vertex. In this case G is called Eulerian. We denote the indegree of a vertex v by deg(v).