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...]], a weighted [[undirected graph]] connecting a set of [[point (geometry)|geometric points]] with the property that, for every pair of points in the graph, the [[Andrew Yao]] used these graphs to construct high-dimensional [[Euclidean minimum spanning tree]]s.<ref nam ...

* the family of 20 graphs generated from the [[complete graph]] <math>K_7</math>. * the family of 78 graphs generated from <math>K_7</math> and <math>K_{3,3,1,1}</math>. ...

...on <math>\ell</math> but not depend on the choice of vertex. Walk-regular graphs can be thought of as a [[spectral graph theory]] analogue of [[vertex-trans ...et/a/264155|title=Are there only finitely many distinct cubic walk-regular graphs that are neither vertex-transitive nor distance-regular?|website=mathoverfl ...

...>{{Cite journal |last=Maehara |first=Hiroshi |date=1984-01-01 |title=Space graphs and sphericity |url=https://dx.doi.org/10.1016/0166-218X%2884%2990113-6 |jo ...st=Maehara |first=Hiroshi |date=1986-03-01 |title=On the sphericity of the graphs of semiregular polyhedra |journal=Discrete Mathematics |language=en |volume ...

...'-semi-Yao graph''' ('''''k''-SYG''') of a set of ''n'' objects ''P'' is a geometric proximity graph, which was first described to present a [[kinetic data stru ...N.|last4= Ilcinkas|first4= D.| year =2010|title= Connections between theta-graphs, Delaunay triangulations, and orthogonal surfaces|book-title= Graph Theoret ...

In [[graph theory]], the '''McKay–Miller–Širáň graphs''' are an infinite class of [[vertex-transitive graph]]s with [[Diameter (g ...l number of vertices can be at most <math>d^2+1</math>. However, only four graphs are known to reach this bound: a single edge (degree one), a 5-vertex [[cyc ...

...lyhedron]]. Alternatively, in purely graph-theoretic terms, the polyhedral graphs are the [[k-vertex-connected graph|3-vertex-connected]], [[planar graph]]s. ...ze]] the polyhedral graphs: they are exactly the 3-vertex-connected planar graphs. That is, whenever a graph is both planar and 3-vertex-connected, there exi ...

Although bouquets have a very simple structure as graphs, they are of some importance in [[topological graph theory]] because their ...p theory]], every [[Cayley graph|Cayley–Serre graph]] (a variant of Cayley graphs with doubled edges) can be represented as the [[covering graph]] of a bouqu ...

...s)|reversed]] by the permutation. Permutation graphs may also be defined [[Geometric graph theory|geometrically]], as the [[intersection graph]]s of line segmen Permutation graphs have several other equivalent characterizations: ...

...av|date=2011-11-01|title=A Simpler Linear-Time Recognition of Circular-Arc Graphs|journal=Algorithmica|language=en|volume=61|issue=3|pages=694–737|doi=10.100 ...rdless cycles ''C''₅, ''C''₇, etc., are circular-arc graphs. ...

| journal = [[Graphs and Combinatorics]] ...50.9715}}. Announced at the Japan Conference on Computational Geometry and Graphs, 2009.</ref> ...

...[[degree (graph theory)|degree]] two; that is, it is a [[disjoint union of graphs|disjoint union]] of [[path graph]]s. Linear arboricity is a variant of [[ar ...mathematics)|odd]] degree, as in that case both expressions are equal. For graphs of [[parity (mathematics)|even]] degree it would imply that the linear arbo ...

...mplete bipartite graph]] on the same vertices. The name was given to these graphs by [[Paul Erdős]] and [[András Hajnal]].{{r|e}} The same concept can also be defined in the same way for infinite graphs over two copies of any ordered set of vertices.{{r|e}} ...

...ut according to Grötzsch's theorem only three colors are needed for planar graphs that do not contain three mutually adjacent vertices. ...ot extend from coloring to list coloring: there exist triangle-free planar graphs that are not 3-list-colorable.<ref>{{harvtxt|Glebov|Kostochka|Tashkinov|200 ...

...raph theory)|clique]] connecting the corresponding vertices, unlike planar graphs in which the largest cliques have only four vertices.<ref name="cgp">{{cita | title = Map graphs ...

Every [[edge-transitive graph]] (disallowing graphs with [[isolated vertex|isolated vertices]]) that is not also [[vertex-trans The [[Levi graph]]s of [[Configuration (geometry)|geometric configuration]]s are biregular; a biregular graph is the Levi graph of an ( ...

...ction]] of a [[Lie group]] on a space that involves the [[derivative]]s of graphs of functions in the space. Differential invariants are fundamental in [[pro ...e a distinguished choice of independent variables (or a parameterization), geometric invariants do not. The [[moving frames method]], which is a refinement of ...

...t of vertices, such that the [[Union (mathematics)|union]] of these planar graphs is {{mvar|G}}, then the thickness of {{mvar|G}} is at most {{mvar|k}}.<ref> ...Duncan, [http://cccg.ca/proceedings/2009/cccg09_04.pdf On Graph Thickness, Geometric Thickness, and Separator Theorems], CCCG 2009, Vancouver, BC, August 17–19, ...

}}.</ref> The problem of constructing relative neighborhood graphs in <math>O(n\log n)</math> time, left open by the mismatch between the Urqu [[Category:Geometric graphs]] ...

A '''hyperbolic geometric graph (HGG)''' or '''hyperbolic geometric network (HGN)''' is a special type of [[spatial network]] where (1) latent ...istance yielding the connection probability). A HGG generalizes a [[random geometric graph]] (RGG) whose embedding space is [[Euclidean space|Euclidean.]] ...