0
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 *..............................................
......................................................
Still curious? Ask our experts.
Chat with our AI personalities
Coach
Ross
ViviYes, 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.
Add your answer:
Earn +20 pts
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.
