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A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph . Similar notions may be defined for directed graphs , where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices ...
The Nauru graph [1] has LCF notation [5, –9, 7, –7, 9, –5] 4.. In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle.
This identity's restriction to the case when is unitary, + + = + and =, where is the identity m×m-matrix, makes the (2m+n)×(2m+n)-matrix in the equality's right side unitary and its Hamiltonian cycle polynomial computable, hence, in polynomial time what therefore generalizes the above-given formula for the Hamiltonian cycle polynomial of a ...
A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time.
This is a list of recurring cycles. See also Index of wave articles ... sequence – Fourier series – Frequency domain – Frequency spectrum – Hamiltonian ...
Pages in category "Hamiltonian paths and cycles" The following 23 pages are in this category, out of 23 total. This list may not reflect recent changes. ...
A graph that can be proven non-Hamiltonian using Grinberg's theorem. In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengths of its face cycles. If a graph does not meet this condition, it is not Hamiltonian.
There is always a Hamiltonian cycle in the wheel graph and there are + cycles in W n (sequence A002061 in the OEIS). The 7 cycles of the wheel graph W 4 . For odd values of n , W n is a perfect graph with chromatic number 3: the vertices of the cycle can be given two colors, and the center vertex given a third color.