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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.

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

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The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.

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

Eular

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

Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).Leonhard Euler (after whom it was named).

Related questions

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.

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.

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.

The difference between an Euler circuit and an Euler path is in the execution of the process. The Euler path will begin and end at varied vertices while the Euler circuit uses all the edges of the graph at once.

connecting the vertices in a graph so that the route traveled starts and ends at the same vertex.

An euler path is when you start and one point and end at another in one sweep wirthout lifting you pen or pencil from the paper. An euler circuit is simiar to an euler path exept you must start and end in the same place you started.

Calculus and Graph Theory.

Leonhard Euler is known as a Swiss mathematician and physicist. He made many famously known accomplishments in the area of calculus and graph theory.

a path that starts and ends at the same vertex and passes through all the other vertices exactly once...

no

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

- a problem in NP means that it can be solved in polynomial time with a non-deterministic turing machine - a problem that is NP-hard means that all problems in NP are "easier" than this problem - a problem that is NP-complete means that it is in NP and it is NP-hard example - Hamiltonian path in a graph: The problem is: given a graph as input, an algorithm must say whether there is a hamiltonian path in it or not. in NP: here is an algorithm that works in polynomial time on a non-deterministic turing machine: guess a path in the graph. Check that it is really a hamiltonian path. NP-hard: we use reduction from a problem that is NP-comlete (SAT for example). Given an input for the other problem we construct a graph for the hamiltonian-path problem. The graph should have a path iff the original problem should return "true". Therefore, if there is an algorithm that executes in polynomial time, we solve all the problems in NP in polynomial time.j