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Hamiltonian Graph in Discrete mathematics. The graph will be known as a Hamiltonian graph if there is a closed walk in a connected graph, which passes each and every vertex of the graph exactly once except the root vertex or starting vertex. The Hamiltonian walk must not repeat any edge.
May 5, 2024 · Hamiltonian Cycle or Circuit in a graph G is a cycle that visits every vertex of G exactly once and returns to the starting vertex. If graph contains a Hamiltonian cycle, it is called Hamiltonian graph otherwise it is non-Hamiltonian.
A Hamiltonian graph, also called a Hamilton graph, is a graph possessing a Hamiltonian cycle. A graph that is not Hamiltonian is said to be nonhamiltonian. A Hamiltonian graph on n nodes has graph circumference n. A graph possessing exactly one Hamiltonian cycle is known as a uniquely Hamiltonian graph.
Aug 23, 2019 · Hamiltonian graph - A connected graph G is called Hamiltonian graph if there is a cycle which includes every vertex of G and the cycle is called Hamiltonian cycle. Hamiltonian walk in graph G is a walk that passes through each vertex exactly once.
Mar 22, 2022 · A graph \ (\textbf {G} = (V,E)\) is said to be hamiltonian if there exists a sequence \ ( (x_1,x_2,…,x_n)\) so that. for each \ (i = 1,2,...,n-1,x_ix_ {i+1}\) is an edge in \ (\textbf {G}\). Such a sequence of vertices is called a hamiltonian cycle. The first graph shown in Figure 5.16 both eulerian and hamiltonian.
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once.
Hamiltonian Path is a path in a directed or undirected graph that visits each vertex exactly once. A Hamiltonian circuit is a circuit that visits every vertex once with no repeats.
Aug 17, 2021 · A Hamiltonian path through a graph is a path whose vertex list contains each vertex of the graph exactly once, except if the path is a circuit, in which case the initial vertex appears a second time as the terminal vertex.
Just as circuits that visit each vertex in a graph exactly once are called Hamilton cycles (or Hamilton circuits), paths that visit each vertex on a graph exactly once are called Hamilton paths.
A simple graph that has a Hamiltonian cycle is called a Hamiltonian graph. We observe that not every graph is Hamiltonian; for instance, it is clear that a dis-connected graph cannot contain any Hamiltonian cycle/path. There are also connected graphs that are not Hamiltonian.
