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Graph which can be made planar by removing a single node
an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs K5 or
Apex_graph
Graph that can be embedded in the plane
planar graph has a Hamiltonian cycle. An apex graph is a graph that may be made planar by the removal of one vertex, and a k-apex graph is a graph that
Planar_graph
Topics referred to by the same term
peroxide Apex (geometry), the highest vertex in a polyhedron or the point where the two equal sides of an isosceles triangle meet Apex graph, a graph that
Apex
Cubic graph with 8 vertices and 12 edges
graph. As a Möbius ladder, the Wagner graph is nonplanar but has crossing number one, making it an apex graph. It can be embedded without crossings on
Wagner_graph
Embedding a graph in 3D space with no cycles interlinked
linklessly embeddable graphs have the Petersen family graphs as their forbidden minors, and include the planar graphs and apex graphs. They may be recognized
Linkless_embedding
triangle. apex 1. An apex graph is a graph in which one vertex can be removed, leaving a planar subgraph. The removed vertex is called the apex. A k-apex graph
Glossary_of_graph_theory
-minor-free graph is an apex graph Does a Moore graph with girth 5 and degree 57 exist? Do there exist infinitely many strongly regular geodetic graphs, or any
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Describing a family of graphs by excluding certain (sub)graphs
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to
Forbidden graph characterization
Forbidden_graph_characterization
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges
Graph_minor
Cycle graph with all opposite nodes linked
a nonplanar apex graph, meaning that it cannot be drawn without crossings in the plane but removing one vertex allows the remaining graph to be drawn
Möbius_ladder
Vertex adjacent to all others in a graph
logic of graphs, and for apex graphs. Graphs that contain a universal vertex include the stars, trivially perfect graphs, and friendship graphs. For wheel
Universal_vertex
Theorem relating graph minors and topological embeddings
In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between
Graph_structure_theorem
Family of 7 undirected graphs
In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K6. The Petersen family
Petersen_family
Number denoting a graph's closeness to a tree
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest
Treewidth
Binary operation in graph theory
planar graphs, extensions of these results have been proven for graphs of bounded genus, graphs with a forbidden minor that is an apex graph, bounded-degree
Strong_product_of_graphs
planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the graph minor
Bidimensionality
Finiteness of sets of forbidden graph minors
graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph minor
Robertson–Seymour_theorem
Polyhedron with 7 faces
which are erected six isosceles triangular faces that meet at a point (the apex). Like any pyramid, it is self-dual. A hexagonal pyramid has seven vertices
Hexagonal_pyramid
On tangency patterns of circles
whose interiors are disjoint. The intersection graph of a circle packing, called a coin graph, is the graph having a vertex for each circle, and an edge
Circle_packing_theorem
Size of largest complete graph made by contracting edges of a given graph
eight-vertex Wagner graph. The graphs with Hadwiger number at most five include the apex graphs and the linklessly embeddable graphs, both of which have
Hadwiger_number
Solid with eight equal triangular faces
octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example of a four-connected
Regular_octahedron
Graph theory concept
In graph theory, a planar cover of a finite graph G is a finite covering graph of G that is itself a planar graph. Every graph that can be embedded into
Planar_cover
The k-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 structure for
Semi-Yao_graph
Conic solid with a polygonal base
formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic
Pyramid_(geometry)
Convex polyhedron with six faces with four edges each
between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube. General cuboids have many different types
Cuboid
Polyhedron with 8 triangles and 6 squares
positions. The graph of a cuboctahedron may be constructed as the line graph of the cubical graph, making it becomes the locally linear graph. The 24 edges
Cuboctahedron
Town in Qalyubia, Egypt
eg. 27 August 2017. "Climate: Al Qanatir al Khairiya - Climate graph, Temperature graph, Climate table". Climate-Data.org. Retrieved 2014-01-03. v t e
El_Qanater_El_Khayreya
Solid with twenty equal triangular faces
is an example of a Platonic solid and of a deltahedron. The icosahedral graph represents the skeleton of a regular icosahedron. Many polyhedra and other
Regular_icosahedron
Gluing graphs at complete subgraphs
omit a small number of apexes (vertices that may be connected to an arbitrary subset of the other vertices) and vortices (graphs with low pathwidth that
Clique-sum
Examination of the heart's electrical activity
shows a line graph of the heart's electrical activity through repeated cardiac cycles. It is an electrogram of the heart which is a graph of voltage versus
Electrocardiography
System of elements that are subordinated to each other
children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies
Hierarchy
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
graph. Taking any non-comparability graph and adding an apex (a vertex connected to any other vertex), we obtain a non-word-representable graph, which
Word-representable_graph
Mathematical function relating circular and hyperbolic functions
Graph of the Gudermannian function.
Gudermannian_function
Topics referred to by the same term
the first derivative of curvature is zero Vertex (graph theory), the fundamental unit of which graphs are formed Vertex (topography), in a triangulated
Vertex
Polyhedron with four faces
be generally seen as a graph by Steinitz's theorem, known as tetrahedral graph, one of the Platonic graphs. It is complete graph K 4 {\displaystyle K_{4}}
Tetrahedron
Plane curve: conic section
parallel to another plane that is tangential to the conical surface. The graph of a quadratic function y = a x 2 + b x + c {\displaystyle y=ax^{2}+bx+c}
Parabola
Mathematical idealization of the surface of a body
point, the apex, which is outside the plane of the circle) is an algebraic surface which is not a differentiable surface. If one removes the apex, the remainder
Surface_(mathematics)
Graphic procedure in the geochemical interpretation of water-analyses
separate ternary plots. The apexes of the cation plot are calcium, magnesium and sodium plus potassium cations. The apexes of the anion plot are sulfate
Piper_diagram
Interstellar comet in 2025
3I/ATLAS Observations Coordination website 3I/ATLAS Star Chart and Magnitude Graph, by Seiichi Yoshida, updated 25 July 2025 Star Chart, by Gianluca Masi,
3I/ATLAS
Mixed/virtual reality headset
argued that "everything it does, it does well, but it does nothing at the apex of its class", and that the Quest 3 "might not be enough to make mainstream
Meta_Quest_3
Foods called nuts, which may be true nuts or seeds, drupes or legumes
Graph of nutritional properties of nuts and oily seeds
Nut_(food)
Reciprocating internal combustion engine
engine and car were both shown at the 1963 Tokyo Motor Show. Hollow cast iron apex seals reduced vibration by changing their resonance frequency and thus eliminated
Mazda_Wankel_engine
Type of diagram
consist of three different graphs: flow-density, speed-flow, and speed-density. The graphs are two dimensional graphs. All the graphs are related by the equation
Fundamental diagram of traffic flow
Fundamental_diagram_of_traffic_flow
Study of optimal transportation and allocation of resources
construct a graph of y ↦ c ( x , y ) {\displaystyle y\mapsto c(x,y)} apexed at ( x , − ψ ( x ) ) {\displaystyle (x,-\psi (x))} . That is, it is the graph of y
Transportation theory (mathematics)
Transportation_theory_(mathematics)
4-D polyhedral pyramid
octahedron on the base and 8 triangular pyramid cells which meet at the apex. Since an octahedron has a circumradius divided by edge length less than
Octahedral_pyramid
Proprietary database management system
within a single engine, including relational, JSON document, XML, spatial, graph, text, and vector data, all queryable through SQL. Oracle Database runs
Oracle_Database
3D animation software
animation, audio, or a combination of these and custom formats. This node graph architecture is similar (in some contexts) to that employed in node-based
Houdini_(software)
ML Alma-0 AmbientTalk Amiga E AMPL Analitik AngelScript Apache Pig latin Apex (Salesforce.com, Inc) APL App Inventor for Android's visual block language
List_of_programming_languages
Curve from a cone intersecting a plane
l is the semi-latus rectum. As above, for e = 0, the graph is a circle, for 0 < e < 1 the graph is an ellipse, for e = 1 a parabola, and for e > 1 a hyperbola
Conic_section
Most populous city in Nevada, United States
to around 205 US gallons (780 L; 171 imp gal) in 2015. See or edit raw graph data. Boulder City, incorporated Enterprise, unincorporated Henderson, incorporated
Las_Vegas
Country in Southeast Europe
revolt in 1185 established a Second Bulgarian Empire, which reached its apex under Ivan Asen II (1218–1241). After numerous exhausting wars and feudal
Bulgaria
Bureau of Aircraft Accidents Archives. Retrieved 13 March 2025. "Accidents Graph (1954–2024)". Bureau of Aircraft Accidents Archives. Retrieved 13 March
List of accidents involving sports teams
List_of_accidents_involving_sports_teams
American businessman (born 1969)
numbered event, Zuffa Boxing 01, in January 2026. It was hosted at the Meta Apex in Las Vegas and was headlined by a bout between Callum Walsh and Carlos
Dana_White
Tetrahedron where all three face angles at one vertex are right angles
at one vertex are right angles. That vertex is called the right angle or apex of the trirectangular tetrahedron and the face opposite it is called the
Trirectangular_tetrahedron
List of projects maintained by the Apache Software Foundation
PostgreSQL extension that provides graph database functionality in order to enable users of PostgreSQL to use graph query modeling in unison with PostgreSQL's
List of Apache Software Foundation projects
List_of_Apache_Software_Foundation_projects
to the coordinates of the apex of each tripod. There are no other triangles in these graphs (they are locally linear graphs) because any other triangle
Tripod_packing
Family of dinosaurs
the largest predators in their respective ecosystems, putting them at the apex of the food chain. The largest species was Tyrannosaurus rex, the most massive
Tyrannosauridae
Species of mammal
Graph showing Iberian lynx population in Spain, 1960–2007
Iberian_lynx
Band of audio frequencies that produce the effect of auditory masking in the human ear
auditory filters are found by analysis of psychoacoustic tuning, which are graphs that show a subject's threshold for detection of a tone as a function of
Critical_band
Atmospheric optical phenomenon
of clusters of bullet-shaped ice columns. As light passes through the 60° apex angle of the hexagonal ice prisms, it is deflected twice, resulting in deviation
22°_halo
NASA Mars rover deployed in 2004
Graph of atmospheric opacity and Opportunity's energy reserve
Opportunity_(rover)
Corporate boards of directors strategy
the graph for cut points and failed to find any with their search starting with corporations with large boards. In a study of clustering in the graph, Levin
Interlocking_directorate
US charter/scheduled airline hybrid (1944–1978)
certification by the FAA). The market share of supplementals was small (see Graph 1), but the carriers attracted much attention during the regulated era ending
Supplemental_air_carrier
Technical specification
without self-damage. SOA is usually presented in transistor datasheets as a graph with VCE (collector-emitter voltage) on the abscissa and ICE (collector-emitter
Safe_operating_area
Chinese view of a supreme God
of the "Six Spirits" who were Predynastic Shang male ancestors. The bone graph for Shang Jia consists of a square encompassing a cross. Since the cross
Shangdi
Oceanic division
Research Letters, 43(18), 9749-9756 "Continued Sea Ice Decline in 2005". Graph by Robert Simmon, Earth Observatory, and Walt Meier, NSIDC; photo by Nathaniel
Arctic_Ocean
Graph of space and time in special relativity
graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph,
Spacetime_diagram
Capital city of Ecuador
"Geography". Retrieved 29 March 2013. "Climate: Quito – Climate graph, Temperature graph, Climate table". Climate-Data.org. Retrieved 18 July 2025. "Weather"
Quito
Range of frequencies that can be heard by humans or other animals
vestibular systems. A basic measure of hearing is afforded by an audiogram, a graph of the absolute threshold of hearing (minimum discernible sound level) at
Hearing_range
Field of mathematics dealing with three-dimensional Euclidean spaces
convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube Some sources also require that each of the
Solid_geometry
Polyhedron formed by joining mirroring pyramids base-to-base
two pyramids are mirror images across their common base plane. When each apex (pl. apices, the off-base vertices) of the bipyramid is on a line perpendicular
Bipyramid
SOTA. GRS-QA: Graph Reasoning-Structured Question Answering Dataset. A dataset designed to evaluate question answering models on graph-based reasoning
Language_model_benchmark
Residents of Quebec, Canada
Legislative Assembly to National Assembly in 1968. Nationalism reached an apex in the 1970s and 1990s, with contentious constitutional debates resulting
Québécois_people
Pyramid with a square base
with a square base and four triangles, having a total of five faces. If the apex of the pyramid is directly above the center of the square, it becomes a form
Square_pyramid
Wadi in Oman and UAE
Its main source is situated near the drainage divide, at the northeastern apex of the drainage basin, at an altitude of approximately 1,348 m (4,423 ft)
Wadi_Khabb_(Fujairah)
Four-dimensional analogue of the tetrahedron
apex vertex (which is outside the 3-cube and does not appear in the illustration at all). Although the four additional edges all reach the same apex vertex
5-cell
Earth's southernmost continent
most recent charted data by a few months.) "Charctic Interactive Sea Ice Graph: A Sea Ice Today Tool". National Snow and Ice Data Center. University of
Antarctica
1812 conflict during the Napoleonic Wars
from overwork and vehicles that could not be repaired broke down. As the graph of Charles Joseph Minard, given below, shows, the Grande Armée incurred
French_invasion_of_Russia
Highest court in the State of Israel
poll graph on State institutions "IDI Releases 2016 Israeli Democracy Index". en.idi.org.il. Retrieved September 20, 2018. – Direct link to poll graph on
Supreme_Court_of_Israel
Flat-sided three-dimensional shape
purely graph-theoretic characterization of the skeletons of convex polyhedra: it states that the skeleton of every convex polyhedron is a planar graph with
Polyhedron
Mass extinction event about 66 million years ago
insufficient methods for accurate replication and problematic isotopic graphs with irregular data and error bars. A study of fossilized fish bones found
Cretaceous–Paleogene extinction event
Cretaceous–Paleogene_extinction_event
Polyhedron with 6 faces
that convex polyhedra have vertices and edges that form 3-vertex-connected graphs. For other types of polyhedra that allow faces that are not simple polygons
Hexahedron
Species of fish
by November of their first year.[citation needed] Adult muskellunge are apex predators where they occur naturally. Only humans and (rarely) large birds
Muskellunge
Genus of Late Cretaceous theropod
largest carnivore in its environment, Tyrannosaurus rex was most likely an apex predator, preying upon hadrosaurs, juvenile armored herbivores like ceratopsians
Tyrannosaurus
Convex polyhedron with 12 triangular faces
Parish, James L.; Traub, Cynthia M.; Weyhaupt, Adam G. (2013), "Coloring graphs to classify simple closed geodesics on convex deltahedra." (PDF), International
Snub_disphenoid
Sphere tangent to every edge of a polyhedron
canonical polyhedron for a given polyhedral graph can be constructed by representing the graph and its dual graph as perpendicular circle packings in the
Midsphere
Plane curve: conic section
intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Besides being a conic section
Hyperbola
Point to which functions converge in analysis
variable, this is the limiting value of the slope of secant lines to the graph of a function. Although implicit in the development of calculus of the 17th
Limit_of_a_function
Family of digital modulation methods
Retrieved 2024-10-09.{{cite web}}: CS1 maint: others (link) "TrangoLink Apex Orion - Trango Systems". www.trangosys.com. Archived from the original on
Quadrature amplitude modulation
Quadrature_amplitude_modulation
UNESCO World Heritage Site in southern Egypt
Retrieved 2011-11-20. Britannica, p.756 "Climate: Abu Sinbil – Climate graph, Temperature graph, Climate table". Climate-Data.org. Retrieved 14 August 2013. "Abu
Abu_Simbel
Rapid decrease in Earth's biodiversity
in the following section. The "Big Five" mass extinctions are bolded. a Graphed but not discussed by Sepkoski (1996), considered continuous with the Late
Extinction_event
Pyramid with a pentagon base
the lateral edges of the pyramid, meeting at the sixth vertex called the apex. A pentagonal pyramid is said to be regular if its base is circumscribed
Pentagonal_pyramid
1983 aircraft shotdown over the Sea of Japan
that KAL 007 would "descend to 10,000" [feet; 3,000 m]. At 18:27:20, ICAO graphing of Digital Flight Data Recorder tapes showed that after a descent phase
Korean_Air_Lines_Flight_007
2019 Android mobile operating system
"recommended" but optional. Selected modules within this system use the new APEX package format, a variation of APK files designed to host and run low-level
Android_10
Extinction of large animals at the end of the last Ice Age
terrestrial mekosuchine crocodilian, apex predator) Volia (a two-to-three meter long mekosuchine crocodylian, apex predator of Pleistocene Fiji) Mekosuchus
Late_Pleistocene_extinctions
Highest mountain in the Northeastern US
also the snowiest month on record with 172.8 in (4.39 m). See or edit raw graph data. Mount Washington is underlain by Devonian-era banded schist and quartzite
Mount_Washington
first-order PDE. Consider the graph of a solution surface in R × M {\displaystyle \mathbb {R} \times M} . The tangent to the graph at a fixed point u , q {\displaystyle
Monge_equation
Four-dimensional analog of the dodecahedron
adjacency matrix of the vertices representing the polyhedral graph of the unit-radius 120-cell, the graph diameter is 15, connecting each vertex to its coordinate-negation
120-cell
Spectroscopic technique
the excitation spot (apex of the tip). The mode can propagate along the tip without producing any radiation field up to the tip apex where it interacts
Raman_spectroscopy
APEX GRAPH
APEX GRAPH
Girl/Female
Indian
Queen of the apes.
Female
Egyptian
, the wife and daughter of Rameses-Miamun.
Surname or Lastname
Americanized spelling of Swedish Ap(p)elberg, an ornamental name composed of the elements apel ‘apple tree’ + berg ‘mountain’.English
Americanized spelling of Swedish Ap(p)elberg, an ornamental name composed of the elements apel ‘apple tree’ + berg ‘mountain’.English : the surname Applebury is recorded in England in the 19th century, perhaps a habitational name from a lost place.
Female
Egyptian
, the hippo goddess.
Male
English
Short form of English unisex Alex, LEX means "defender of mankind."
Boy/Male
American, Australian, British, Celebrity, Chinese, Danish, Dutch, English, Finnish, French, German, Greek, Hebrew, Indian, Irish, Jamaican, Latin, Sindhi, Swedish, Swiss, Tamil
Form of Alexander; Helper and Defender of Mankind
Boy/Male
Greek American English
Defender of men; protector of mankind.
Female
English
Variant spelling of English unisex Alex, ALYX means "defender of mankind."
Male
Greek
(Άποφις) Greek form of Egyptian Apep, possibly APOPHIS means "to slither." In mythology, Apep is the personification of evil, seen as a giant snake, serpent or dragon. Known as the Serpent of the Nile or Evil Lizard, he was an enemy of the sun god.Â
Male
Egyptian
, the son of Ape.
Male
English
English unisex short form of Alexandra and Alexander, ALEX means "defender of mankind."Â
Surname or Lastname
German (also Gräff), Dutch, and Jewish (Ashkenazic)
German (also Gräff), Dutch, and Jewish (Ashkenazic) : variant of Graf.English : metonymic occupational name for a clerk or scribe, from Anglo-Norman French grafe ‘quill’, ‘pen’ (a derivative of grafer ‘to write’, Late Latin grafare, from Greek graphein).
Female
Egyptian
, an Egyptian lady.
Girl/Female
Arabic, Muslim
Peak; Height; Apex; Climax
Male
English
Variant spelling of English unisex Alex, ALIX means "defender of mankind."
Girl/Female
Indian
Expectation
Girl/Female
Tamil
Expectation
Girl/Female
American, Chinese, Finnish, French, German, Greek, Indian, Irish, Sikh
Defender of Mankind; Noble; Female Version of Alexander
Male
Egyptian
, ape, or imitator.
Girl/Female
Greek American
A feminine form of Alexander meaning defender of men, used in Britain since early 13th century....
APEX GRAPH
APEX GRAPH
Surname or Lastname
English
English : occupational name for a maker of wooden furniture, Anglo-Norman French joignour (Old French joigneor, from joinre ‘to join’, ‘to connect’, Latin iungere).
Boy/Male
Hindu, Indian, Tamil
Younger
Girl/Female
Hindi
Dancer.
Girl/Female
Indian
White
Boy/Male
Hindu, Indian
Happy
Boy/Male
Hindu, Indian
God of Everyone
Boy/Male
Hindu, Indian, Sanskrit
Supporter of Knowledge
Boy/Male
Hindu, Indian
Thought
Girl/Female
Hindu
A name of river
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Earth
APEX GRAPH
APEX GRAPH
APEX GRAPH
APEX GRAPH
APEX GRAPH
n.
One who imitates servilely (in allusion to the manners of the ape); a mimic.
a.
Bounded like a nipple; -- said of the apex of some shells.
imp. & p. p.
of Ape
a.
Situated at, or near, the apex; apical.
a.
Being under the apex; of or pertaining to the part just below the apex.
n.
A turning point; the principal or highest point; top; summit; crown; apex.
a.
Pierced at the apex.
a.
At or belonging to an apex, tip, or summit.
a.
Conical, but having the apex downward; inversely conical.
n.
A quadrumanous mammal, esp. of the family Simiadae, having teeth of the same number and form as in man, and possessing neither a tail nor cheek pouches. The name is applied esp. to species of the genus Hylobates, and is sometimes used as a general term for all Quadrumana. The higher forms, the gorilla, chimpanzee, and ourang, are often called anthropoid apes or man apes.
p. pr. & vb. n.
of Ape
a.
Lacking the apex; -- said of certain spiral shells in which the apex naturally drops off.
n.
The tip, top, point, or angular summit of anything; as, the apex of a mountain, spire, or cone; the apex, or tip, of a leaf.
v. t.
To mimic, as an ape imitates human actions; to imitate or follow servilely or irrationally.
n.
The end or edge of a vein nearest the surface.
n.
One who apes.
n.
The apex of the last abdominal segment of an insect.
pl.
of Apex
pl.
of Apex
n. pl.
See Apex.