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  1. How many Hamiltonian cycles are there in a complete graph $K_n$ ($n ...

    There are $\frac {n-1} {2}$ such consecutive pairs in the upper half of the circumference with $\frac {n-1} {2}$ edges connecting them each leading to unique edge disjoint Hamiltonian circuits.

  2. Is the Hamiltonian always the total energy? - Physics Forums

    Apr 29, 2016 · The Hamiltonian is not always equivalent to the total energy of a system in classical mechanics. While it is often identified with total energy, exceptions arise in specific scenarios, such …

  3. discrete mathematics - What is the difference between a Hamiltonian ...

    Aug 18, 2020 · Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once Hamiltonian cycle is a Hamiltonian path that is a cycle, and a cycle is closed trail in …

  4. What Is the Difference Between Hamiltonian and Hermitian Operators?

    Oct 5, 2010 · The discussion revolves around the distinction between Hamiltonian and Hermitian operators, focusing on their definitions, properties, and implications in quantum mechanics and …

  5. If the subdivision of a graph $G$ is Hamiltonian, is $G$ Eulerian?

    Nov 3, 2025 · $G$ has a vertex of degree $0$ or $1$ (in which case, the same is true of the subdivision - but a Hamiltonian graph must have minimum degree $2$); $G$ has a vertex of degree $3$ or more.

  6. Hamilton paths/cycles in grid graphs - Mathematics Stack Exchange

    This is trivially Hamiltonian in that there is a zero length path that visits the vertex. [1] Part 3: If m = 1 xor n = 1, the graph is not Hamiltonian All Hamiltonian graphs are biconnected. [2] If exactly one of the …

  7. Time-dependent unitary transformations of the Hamiltonian

    Oct 17, 2019 · The discussion revolves around the transformation of the Hamiltonian operator under time-dependent changes of basis in quantum mechanics. Participants explore the implications of …

  8. Why is the complete graph $K_2$ not Hamiltonian?

    May 11, 2020 · You seem to want a Hamiltonian cycle. Details of paths, cycles, trails, walks, et c. depend on one's definitions. Hamiltonian path : "A Hamiltonian cycle (or Hamiltonian circuit) is a …

  9. Separable Hamiltonian for central potential - Physics Forums

    May 14, 2022 · The discussion revolves around the separability of the Hamiltonian in the context of a central potential problem in quantum mechanics. Participants explore how to express the …

  10. What are the main differences between Hamiltonian and Lagrangian ...

    Aug 13, 2014 · The discussion clarifies the fundamental differences between Hamiltonian and Lagrangian mechanics. The Lagrangian formulation focuses on the principle of least action, …