Search results

[[Category:Extensions and generalizations of graphs]] ...

...nalizing one or more vertices in a [[graphical model]] that takes the form of a [[directed acyclic graph]]. ...vertex to another, bidirected edges, which have an arrowhead at both ends, and undirected edges, which have no arrowheads. It is required to satisfy some ...

...ng {{mvar|n}} edges is called the {{nowrap|size-{{mvar|n}}}} dipole graph, and is denoted by {{math|D{{sub|''n''}}}}. The {{nowrap|size-{{mvar|n}}}} dipol ...amond crystal]] as an abstract graph is the maximal abelian covering graph of {{math|D{{sub|4}}}}. ...

...of ''e'' (in some indicated direction). A gain graph is a generalization of a [[signed graph]], where the gain group ''G'' has only two elements. See ...h a '''weight''' on an edge, whose value is independent of the orientation of the edge. ...

{{Short description|Construction of combinatorial group theory}} In [[mathematics]], the '''HNN extension''' is an important construction of [[combinatorial group theory]]. ...

{{Short description|Assignment of labels to elements of a graph}} ...to [[edge (graph theory)|edges]] and/or [[vertex (graph theory)|vertices]] of a [[Graph (discrete mathematics)|graph]].<ref name=mathw>{{mathworld|Labele ...

[[File:Bidirected graph features.svg|thumb|360px|The different types of edge in a bidirected graph]] In the [[mathematics|mathematical]] domain of [[graph theory]], a '''bidirected graph''' (introduced by {{harvnb|Edmonds| ...

...ngly regular graph]]s, and also [[finite group]]s because many regular two-graphs have interesting [[automorphism group]]s. ...lled '''2-graphs''' in [[graph theory]], such as [[regular graph|2-regular graphs]]. ...

...ber of its parents, and the width of an ordered graph is the maximal width of its nodes. ...d outlined below. The '''induced width''' of an ordered graph is the width of its induced graph.<ref>Page 87 Dechter. (2003). Constraint Processing</ref> ...

...tation|first=Daniel|last=Zwillinger|title=CRC Standard Mathematical Tables and Formulae, 32nd Edition|year=2011|publisher=CRC Press|isbn=978-1-4398-3550-0 | journal = [[Transactions of the American Mathematical Society]] ...

...ways that signs can be assigned to the sides of a triangle. An odd number of negative signs makes an unbalanced triangle, according to [[Fritz Heider]]' In the area of [[graph theory]] in [[mathematics]], a '''signed graph''' is a graph in whi ...

...e:Multi-pseudograph.svg|thumb|right|A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops.]] ...1997, p. 1 or Chartrand and Zhang 2012, p. 26.</ref>), that is, [[Glossary of graph theory#Basics|edges]] that have the same [[Vertex (graph theory)|end ...

{{Short description|Matrix representation of a graph}} ...Simon Laplace]], the graph Laplacian matrix can be viewed as a matrix form of the negative [[discrete Laplace operator]] on a graph approximating the neg ...

{{Short description|Graph representing edges of another graph}} ...')}} that represents the adjacencies between [[edge (graph theory)|edges]] of {{mvar|G}}. {{math|L(''G'')}} is constructed in the following way: for eac ...

...as {{mvar|n}}.<ref name="callan">{{cite arXiv|title=A combinatorial survey of identities for the double factorial|first=David|last=Callan|eprint=0906.131 ...liant Math & Science Wiki|url=https://brilliant.org/wiki/double-factorials-and-multifactorials/|access-date=2020-09-10|website=brilliant.org|language=en-u ...

...''R''(''r'', ''s'')}} signifies an integer that depends on both {{mvar|r}} and {{mvar|s}}.) ...ence of ''monochromatic subsets'', that is, [[subset]]s of connected edges of just one colour. ...

...of pets to humans such that the maximum number of pets are adopted by one of its preferred humans.]] ...ssary of graph theory#Direction|sink]] t) is equal to the minimum capacity of an [[Cut (graph theory)|s-t cut]] (i.e., cut severing s from t) in the netw ...

...ath can be dropped: any polygonal path, closed or open, of arbitrary slope and with turning points that are allowed to be placed anywhere, still requires ...first1=George Grantham |author-link=George Grantham Bain |title=The Prince of Puzzle-Makers. An Interview with Sam Loyd. |magazine=[[The Strand Magazine] ...

[[Image:Sperner2d.svg|thumb|upright=1.2|The two-dimensional case of Sperner's lemma: a Sperner coloring, with its 3-colored triangles shaded]] ...tes that every '''Sperner coloring''' (described below) of a triangulation of an {{nowrap|<math>n</math>-dimensional}} [[simplex]] contains a cell whose ...

...ns are leveraged, including '''node consistency''', '''arc consistency''', and '''path consistency'''. ...hening constraints, or creating new constraints. This leads to a reduction of the search space, making the problem easier to solve by some algorithms. Co ...