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# Hamiltonian Circuit -- from Wolfram MathWorld.

See also Hamiltonian path, Euler cycle, vehicle routing problem, perfect matching. Note: A Hamiltonian cycle includes each vertex once; an Euler cycle includes each edge once. Also known as a Hamiltonian circuit. Named for Sir William Rowan Hamilton 1805-1865. Author: PEB. Implementation Fortran, C, Mathematica, and C. Mathematica » The 1 tool for creating Demonstrations and anything technical. WolframAlpha » Explore anything with the first computational knowledge engine. The Hamiltonian is named after William Rowan Hamilton, who created a revolutionary reformulation of Newtonian mechanics, now called Hamiltonian mechanics, which is also important in quantum physics. Introduction. The Hamiltonian is the sum of the kinetic energies of all the particles, plus the potential energy of the particles associated with.

6 –Euler Circuits and Hamiltonian Cycles William T. Trotter trotter@math.. EulerTrails and Circuits Definition A trail x 1, x 2, x 3, , x t in a graph G is called an Euler trail in G if for every edge e of G, there is a unique i with 1 ≤ i < t so that e = x i x. Definition 5.3.1 A cycle that uses every vertex in a graph exactly once is called a Hamilton cycle, and a path that uses every vertex in a graph exactly once is called a Hamilton path. Unfortunately, this problem is much more difficult than the corresponding Euler circuit and walk problems; there is no good characterization of graphs with. The best Hamilton circuit for a weighted graph is the Hamilton circuit with the least total cost. A complete graph is a graph where each vertex is connected to every other vertex by an edge. In the mathematical field of graph theory, a Hamiltonian path or traceable path is a path in an undirected graph that visits each vertex exactly once. A Hamiltonian cycle or Hamiltonian circuit is a Hamiltonian path that is a cycle. Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete. For example, let's look at the following graphs some of which were observed in earlier pages and determine if they're Hamiltonian.

Definition 4: The out-degree of a vertex in a directed graph is the number of edges outgoing from that vertex. The condition that a directed graph must satisfy to have an Euler circuit is defined by the following theorem. Theorem 4: A directed graph G has an Euler circuit iff it is connected and for every vertex u in G in-degreeu = out-degreeu. Hamiltonian synonyms, Hamiltonian pronunciation, Hamiltonian translation, English dictionary definition of Hamiltonian. n. Abbr. H A mathematical function that can be used to generate the equations of motion of a dynamic system, equal for many such systems to the sum of the. Looking for Directed Hamiltonian circuit? Find out information about Directed Hamiltonian circuit. A path along the edges of a graph that traverses every vertex exactly once and terminates at its starting point. Also known as Hamiltonian circuit;. Explanation of Directed Hamiltonian circuit. Nov 03, 2015 · A brief explanation of Euler and Hamiltonian Paths and Circuits. This assumes the viewer has some basic background in graph theory. The. Hamilton circuits Section 2.2 Under what circumstances can we be sure a graph has a Hamilton circut? Theorem 1. K n has a Hamilton circuit for n 3. Proof. Let v 1;:::;v n be any way of listing the vertices in order. Then v 1 v 2 v n v 1 is a Hamilton circuit since all edges are present. In general, having lots of edges makes it easier to have a Hamilton circuit.

## 6 Euler Circuits and Hamiltonian Cycles.

May 16, 2017 · Part-17 hamiltonian graphs in graph theory in hindi discrete mathematics cycle path circuit - Duration: 10:35. KNOWLEDGE GATE 165,203 views.