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What is a Hamiltonian Circuit?

Updated: 4/28/2022
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a path that starts and ends at the same vertex and passes through all the other vertices exactly once...

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Q: What is a Hamiltonian Circuit?
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What is the difference between a Hamiltonian circuit and a Euler circuit?

In an Euler circuit we go through the whole circuit without picking the pencil up. In doing so, the edges can never be repeated but vertices may repeat. In a Hamiltonian circuit the vertices and edges both can not repeat. So Avery Hamiltonain circuit is also Eulerian but it is not necessary that every euler is also Hamiltonian.


What is a hamiltonian path in a graph?

A path along the edges of a graph that traverses every vertex exactly once and terminates at its starting point. Also known as Hamiltonian circuit; Hamiltonian cycle.


What are Hamiltonian equations?

Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.


Can a graph have an Euler circuit but not a Hamiltonian circuit?

Yes. An example: _____A---------B________ A connected directly to B and D by one path. _____|_______/|\________ B connected directly to A and E by one path, and to C by two paths. _____|______/_|_\_______ _____|_____/___\_|______ _____|__E/_____\|______ E connected directly to B and D by one path. _____|____\_____C______ C connected directly to B and D by two paths. _____|_____\____|\_____ _____|______\___|__\___ _____|_______\__|__/___ _____|________\_|_/____ _____|_________\|/_____ _____-------------D_____ D connected directly to A and E by one path, and to C by two paths. There is an Euler circuit: ABCDEBCDA But a Hamiltonian circuit is impossible: as part of a circuit A can only be reached by the path BAD, but once BAD has been traversed it is impossible to get to both C and E without returning to B or D first. However there is a Hamiltonian Path: ABCDE.


What is the proper adjective for Hamilton?

Hamiltonian is the proper adjective for Hamilton. For instance: The Hamiltonian view on the structure of government was much different from that of Jefferson.


What is Hamiltonian function?

The total energy of the system simply described in classical mechanics called as Hamiltonian.


What has the author A Ciampi written?

A. Ciampi has written: 'Classical hamiltonian linear systems' -- subject(s): Dynamics, Hamiltonian systems


Was John Q Adams a Hamiltonian?

no


What were the hamiltonian ideas?

the Hamiltonian idea was the government is to have complete control of all decisions. an that everyone was controlled like big borther in 1984


Is momentum hamiltonian operator is hermitian operator?

The hamiltonian operator is the observable corresponding to the total energy of the system. As with all observables it is given by a hermitian or self adjoint operator. This is true whether the hamiltonian is limited to momentum or contains potential.


Hamiltonian vision of the new nation?

The Hamiltonian vision of the new nation was focused on the establishment of a sovereign nation that would be able to step out from the shadows on Great Britain.


How did Hamilton Feel about the division power between the federal government and the states?

Alexander Hamilton was a Federalist. He and his backers were called the "Hamiltonian's" as opposed to Thomas Jefferson's form of government. He and his followers were called the "Jeffersonians."-The Hamiltonian's wanted a very strong central government as they admired the English aristocracy and the English system of government and wished to see it used as a model.-Hamiltonian's considered the common people ignorant and incapable of self-government.-Hamiltonian's desired high voting qualifications, claiming that unfettered democracy was anarchy.-Hamiltonian's favored a broad interpretation of the Constitution to strengthen the central government at the expense of of state's rights.-Hamiltonian's wanted an expanding bureaucracy.-Hamiltonian's, under certain circumstances, favored restrictions on speech and the press.