Search results
Results from the WOW.Com Content Network
In graph theory, a branch of mathematics, a periodic graph with respect to an operator F on graphs is one for which there exists an integer n > 0 such that F n (G) is isomorphic to G. [1] For example, every graph is periodic with respect to the complementation operator , whereas only complete graphs are periodic with respect to the operator ...
K 4 as the half-square of a cube graph. The half-square of a bipartite graph G is the subgraph of G 2 induced by one side of the bipartition of G. Map graphs are the half-squares of planar graphs, [18] and halved cube graphs are the half-squares of hypercube graphs. [19] Leaf powers are the subgraphs of powers of trees induced by the leaves of ...
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,... In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices, with predicates for equality and adjacency testing.
An aperiodic graph. The cycles in this graph have lengths 5 and 6; therefore, there is no k > 1 that divides all cycle lengths. A strongly connected graph with period three. In the mathematical area of graph theory, a directed graph is said to be aperiodic if there is no integer k > 1 that divides the length of every cycle of the graph.
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. [1] If the graph does not contain any cycles (that is, it is a forest), its girth is defined to be infinity. [2] For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The curve is a cycloid, and the time is equal to π times the square root of the radius of the circle which generates the cycloid, over the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve , which is also a cycloid.
[1] [2] A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas.