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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.
Since the graph corresponding to historical Königsberg has four nodes of odd degree, it cannot have an Eulerian path. An alternative form of the problem asks for a path that traverses all bridges and also has the same starting and ending point. Such a walk is called an Eulerian circuit or an Euler tour. Such a circuit exists if, and only if ...
Euler stated the fundamental results for this problem in terms of the number of odd vertices in the graph, which the handshaking lemma restricts to be an even number. If this number is zero, an Euler tour exists, and if it is two, an Euler path exists. Otherwise, the problem cannot be solved.
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.
Hemifacial spasm (HFS) is a rare neuromuscular disease characterized by irregular, involuntary muscle contractions on one side (hemi-) of the face (-facial). [1] The facial muscles are controlled by the facial nerve (seventh cranial nerve), which originates at the brainstem and exits the skull below the ear where it separates into five main branches.
When your right eye is twitching, it could be due to stress, fatigue or even dry eyes. Unless there's an underlying medical condition, eye twitches tend to come and go like the wind.
Blepharospasm is often associated with dry eyes, but the causal mechanism is still not clear. [16] [8] Research in New York and Italy suggests that increased blinking (which may be triggered by dry eyes) leads to blepharospasm. [24] [25] A case control study in China found that blepharospasm aggravated dry eyes. [26]
One of the main triggers of an eye twitch is stress. For premium support please call: 800-290-4726 more ways to reach us