For completeness of the presentation of both particular questions and the general area, it also contains some material on closely related topics such as traceable, pancyclic and Hamiltonian connected graphs.
The extended abstract of this paper was presented at MFCS '92 (Lecture Notes in Computer Science, Vol.
For example, the smallest polyhedral graph that is not Hamiltonian is the Herschel graph on 11 nodes.
All Platonic solids are Hamiltonian (Gardner 1957), as illustrated above.
(Phys.org)—Researchers have discovered that the solutions to a famous mathematical function called the Riemann zeta function correspond to the solutions of another, different kind of function that may make it easier to solve one of the biggest problems in mathematics: the Riemann hypothesis.
"To our knowledge, this is the first time that an explicit—and perhaps surprisingly relatively simple—operator has been identified whose eigenvalues ['solutions' in matrix terminology] correspond exactly to the nontrivial zeros of the Riemann zeta function," Dorje Brody, a mathematical physicist at Brunel University London and coauthor of the new study, told
Louis and Markus Müller of the University of Western Ontario, have published their work in a recent issue of Physical Review Letters.
In this paper, we use the cycles of a cycle basis to replace the faces and obtain an equality of inner faces in Grinberg theorem, called Grinberg equation.
We explain why Grinberg theorem can only be a necessary condition of Hamilton graphs and apply the theorem, to be a necessary and sufficient condition, to simple graphs.
Once this is done, you know that edge go from lower index vertices to higher.
This means that there exists a Hamiltonian path if and only if there are edge between consecutive vertices, e.g. If the graph is not connected then there is no Hamiltonian and this algorithm will detect it, because at least one of the consecutive vertices won't be connected (or else the graph will be connected).