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The right hand side contains (as a factor) the simple second-power law from potential flow theory, applied at the trailing edge near = + From conformal mapping theory, this quadratic map is known to change a half plane in the -space into potential flow around a semi-infinite straight line. Further, values of the power less than 2 will result in ...
In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.
The "pearls" of the title include theorems, proofs, problems, and examples in graph theory.The book has ten chapters; after an introductory chapter on basic definitions, the remaining chapters material on graph coloring; Hamiltonian cycles and Euler tours; extremal graph theory; subgraph counting problems including connections to permutations, derangements, and Cayley's formula; graph ...
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 Lanchester-Prandtl lifting-line theory [1] is a mathematical model in aerodynamics that predicts lift distribution over a three-dimensional wing from the wing's geometry. [2] The theory was expressed independently [ 3 ] by Frederick W. Lanchester in 1907, [ 4 ] and by Ludwig Prandtl in 1918–1919 [ 5 ] after working with Albert Betz and ...
In the mathematical discipline of graph theory, the edge space and vertex space of an undirected graph are vector spaces defined in terms of the edge and vertex sets, respectively. These vector spaces make it possible to use techniques of linear algebra in studying the graph.
A perfect 1-factorization (P1F) of a graph is a 1-factorization having the property that every pair of 1-factors is a perfect pair. A perfect 1-factorization should not be confused with a perfect matching (also called a 1-factor). In 1964, Anton Kotzig conjectured that every complete graph K 2n where n ≥ 2 has a
Example of B-coloring of Shrikhande graph with 6 colors: highlighted nodes have neighbors in each other colors. Since each node is adjacent to another 6, a 7-color B-coloring may be possible. In graph theory, a b-coloring of a graph is a coloring of the vertices where each color class contains a vertex that has a neighbor in all other color ...