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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 Hamiltonian path in a graph is a path that visits every vertex exactly once. It does not need to visit every edge, only every vertex. If a Hamiltonian path exists in a graph, the graph is called a Hamiltonian graph.


Can a graph have a euler circuit but not a hamiltonian circuit?

Yes, a graph can have an Euler circuit (a circuit that visits every edge exactly once) but not have a Hamiltonian circuit (a circuit that visits every vertex exactly once). This can happen when the graph has certain degree requirements that allow for the Euler circuit but prevent the existence of a Hamiltonian circuit.


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 is the meaning of Hc in an Hamiltonian?

In the context of a Hamiltonian, Hc typically refers to the complex conjugate of the Hamiltonian operator. Taking the complex conjugate of the Hamiltonian operator is often done when dealing with quantum mechanical systems to ensure that physical observables are real-valued.


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


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.