Search results
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.
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.
May 5, 2024 · What is Hamiltonian Cycle? 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.
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 every vertex of \(\textbf{G}\) appears exactly once in the sequence \(x_1x_n\) is an edge of \(\textbf{G}\)
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.
It is not always as easy to determine if a graph has a Hamilton cycle as it is to see that it has an Euler circuit, but there is a large group of graphs that we know will always have Hamilton cycles, the complete graphs.
