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Trident curves are cubic plane curves with an ordinary double point in the real projective plane at x = 0, y = 1, z = 0; if we substitute x = x / z and y = 1 / z into the equation of the trident curve, we get
A table or chart of nuclides is a two-dimensional graph of isotopes of the elements, in which one axis represents the number of neutrons (symbol N) and the other represents the number of protons (atomic number, symbol Z) in the atomic nucleus. Each point plotted on the graph thus represents a nuclide of a known or hypothetical chemical element.
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
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.
Barnette's conjecture is an unsolved problem in graph theory, a branch of mathematics, concerning Hamiltonian cycles in graphs. It is named after David W. Barnette , a professor emeritus at the University of California, Davis ; it states that every bipartite polyhedral graph with three edges per vertex has a Hamiltonian cycle.
Applying the Mycielskian repeatedly, starting with the one-edge graph, produces a sequence of graphs M i = μ(M i−1), sometimes called the Mycielski graphs. The first few graphs in this sequence are the graph M 2 = K 2 with two vertices connected by an edge, the cycle graph M 3 = C 5 , and the Grötzsch graph M 4 with 11 vertices and 20 edges.
A cubic (but not bridgeless) graph with no perfect matching, showing that the bridgeless condition in Petersen's theorem cannot be omitted. In the mathematical discipline of graph theory, Petersen's theorem, named after Julius Petersen, is one of the earliest results in graph theory and can be stated as follows: Petersen's Theorem.
In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle , or locally independent graphs.