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Yes.
Example:
....................................................
...A * ...........................................
......|.\ ......................................... eg Euler circuit: ACDCBA
......|...\ ........... --------- .............
......|.....\........./...............\............ The Hamilton circuit is impossible as it has two
......|.......\...../...................\.......... halves (ACD & CD) connected to each other only
......|.........\./.......................\........ at vertex C. Once vertex C has been reached in
......|.......C *........................* D.... one half, it can only be used to start a path in
......|........./.\......................./......... the other half, or complete the cycle in the
......|......./.....\.................../........... current half; or if the path starts at C, it will end
......|...../.........\.............../............. without the other half being visited before C is
......|.../ ........... --------- .............. revisited.
......|./ ...........................................
...B *..............................................
......................................................
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.
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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 does the Hamiltonian system refer to?
The Hamiltonian system refers to a dynamical system in classical mechanics that is described using Hamilton's equations of motion. It is a formalism that combines the equations of motion of a system with a specific function called the Hamiltonian, which represents the total energy of the system. It is widely used in physics and engineering to analyze and model the behavior of complex physical systems.
What is the significance of the area under the curve on a current v voltage graph?
The area under the curve on a current vs. voltage graph represents the amount of electrical energy transferred. It indicates the work done in moving charge carriers through the circuit. This can be used to calculate power dissipation or energy consumption in the circuit.
How does the graph vary between voltage and current?
In an electrical circuit, the relationship between voltage and current is typically linear, following Ohm's Law (V = IR). This means that as voltage increases, current also increases proportionally, resulting in a straight line graph. The slope of the line is determined by the resistance in the circuit.
How do you derive graphene's low-energy Hamiltonian?
To derive graphene's low-energy Hamiltonian, one typically starts with the tight-binding model for graphene's honeycomb lattice. By applying the nearest neighbor approximation and using certain symmetry properties, one can simplify the model to focus on the low-energy excitations around the Dirac points in the Brillouin zone, leading to a 2x2 matrix Hamiltonian that describes the electronic properties of graphene near the Fermi level.
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.
What is the difference between an Euler circuit and an Euler path?
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.
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.
Find any Hamiltonian circuit on the graph above. Give your answer as a list of vertices, starting and ending at the same vertex. Example: ABCA?
connecting the vertices in a graph so that the route traveled starts and ends at the same vertex.
What is a Euler path or circuit?
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.
What type of math is leonhard euler famous for?
Calculus and Graph Theory.
What are some of the accomplishments of Leonhard Euler?
Leonhard Euler is known as a Swiss mathematician and physicist. He made many famously known accomplishments in the area of calculus and graph theory.
What is a Hamiltonian Circuit?
a path that starts and ends at the same vertex and passes through all the other vertices exactly once...
What is a circuit in graph theory?
no
What are Hamiltonian equations?
Hamiltonian equations are a representation of Hamiltonian mechanics. Please see the link.
What is the difference between NP and NP Complete problems?
- 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
