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Undirected cubic graph derived from a hypercube graph
graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced
Cube-connected_cycles
Archimedean solid with 14 faces
Cube-connected cycles, a family of graphs that includes the skeleton of the truncated cube Chamfered cube, obtained by replacing the edges of a cube with
Truncated_cube
Graphs formed by a hypercube's edges and vertices
graph Cube-connected cycles Fibonacci cube Folded cube graph Frankl–Rödl graph Halved cube graph Hypercube internetwork topology Partial cube Watkins
Hypercube_graph
Form of network configuration
Ultracomputer[citation needed]. Omega network simulation in c Clos network Cube-connected cycles Nonblocking minimal spanning switch Banyan switch Delta network
Omega_network
Topics referred to by the same term
numeral for 300 Countable chain condition, in order theory CCCn, cube-connected cycles of order n in graph theory Continuous curvilinear capsulorhexis
CCC
French computer scientist
was developed. With Franco P. Preparata, he also introduced the cube-connected cycles as a network topology in parallel computing.[D] Vuillemin earned
Jean_Vuillemin
Type of network topology
connected in regular interconnection network such as a de Bruijn graph, a hypercube graph, a hypertree network, a fat tree network, a torus, or cube-connected
Grid_network
Graph where all pairs of vertices are automorphic
edges of the Platonic solids). The finite Cayley graphs (such as cube-connected cycles) are also vertex-transitive, as are the vertices and edges of the
Vertex-transitive_graph
Type of multigraph
rotation and flipping the first bit, can also be used to generate the cube-connected cycles, a different cubic parallel communications network with a greater
Shuffle-exchange_network
the cube-connected cycles. C Cn is an n-vertex cycle graph; see cycle. cactus A cactus graph, cactus tree, cactus, or Husimi tree is a connected graph
Glossary_of_graph_theory
Italian computer scientist
paper (with Jean Vuillemin), still highly cited, presented the cube-connected-cycles (CCC), a parallel architecture that optimally emulates the hypercube
Franco_P._Preparata
Graph defined from a mathematical group
graph Generating set of a group Lovász conjecture Cube-connected cycles Algebraic graph theory Cycle graph (algebra) Proof: Let σ : V ( Γ ) → V ( Γ ) {\displaystyle
Cayley_graph
Solid with six equal square faces
objects are measured. The cube can be represented in many ways. One of them is by drawing a graph with vertices connected with an edge in a plane. Such
Cube
Graph layout on multiple half-planes
thickness of binary de Bruijn graphs, shuffle-exchange graphs, and cube-connected cycles (when these graphs are large enough to be nonplanar) is exactly
Book_embedding
Problem in graph theory
when m is either even or three. In particular this holds for the cube-connected cycles, which can be generated as the Cayley graph of the wreath product
Lovász_conjecture
Solving physical puzzles with speed
puzzle, commonly known as the Rubik's Cube. Participants in this sport are called "speedcubers" (or simply "cubers"), who focus specifically on solving
Speedcubing
3D combination puzzle
Rubik's Cube is a 3D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the
Rubik's_Cube
Primary game controller for the GameCube
The GameCube controller (model number: DOL-003) is the standard game controller for the GameCube video game console, manufactured by Nintendo and launched
GameCube_controller
Graph path which is an induced subgraph
induced cycle is a cycle that is an induced subgraph of G; induced cycles are also called chordless cycles or (when the length of the cycle is four or
Induced_path
Graph representing faces of another graph
these cycles). For edge-weighted planar graphs (with sufficiently general weights that no two cycles have the same weight) the minimum-weight cycle basis
Dual_graph
Graph with a prism as its skeleton
Archimedean graphs. If the two cycles of a prism graph are broken by the removal of a single edge in the same position in both cycles, the result is a ladder
Prism_graph
German-born sculptor, inventor, and mathematician (1898–1979)
platonic solids, including the "invertible cube", which is often sold as an eponymous puzzle, the Schatz cube. From 1927 to his death he lived in Switzerland
Paul_Schatz
Graph with all vertices of degree 4
Herbert (1994), "Uniqueness of maximal dominating cycles in 3-regular graphs and of Hamiltonian cycles in 4-regular graphs", Journal of Graph Theory, 18
Quartic_graph
Computational problem in graph theory
through thirteen are 190, 376, 736, 1461, 2892. For cycles (the coil-in-the-box problem), a cycle cannot exist in a hypercube of dimension less than two
Snake-in-the-box
Type of optical illusion
loop – Cycles going through a hierarchy Surrealism – International cultural movement (1920s–1950s) Tesseract – Four-dimensional analogue of the cube Tritone
Impossible_object
Isometric subgraph of a hypercube
In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph
Partial_cube
Rubik's puzzle
known as the inventor of the Rubik's Cube. Rubik's Snake was released during 1981 at the height of the Rubik's Cube craze. According to Ernő Rubik: "The
Rubik's_Snake
Argentine-born American mathematician
How many colors are needed for a coloring of the n-cube without monochromatic 4-cycles or 6-cycles? Brouwer, Dejter and Thomassen showed that 4 colors
Italo_Jose_Dejter
Graph of short distances in another graph
case. The cube of every connected graph necessarily contains a Hamiltonian cycle. It is not necessarily the case that the square of a connected graph is
Graph_power
Derived bipartite graph with twice as many nodes as the original graph
bipartite double of G. It should not be confused with a cycle double cover of a graph, a family of cycles that includes each edge twice. The bipartite double
Bipartite_double_cover
House built by psychiatrist Carl Jung
after it. In 1950, on the occasion of his 75th birthday, Jung set up a stone cube on the lakeshore, just west of the tower, inscribing it on three sides. One
Bollingen_Tower
Symmetrical transformations of the cuboctahedron into related uniform polyhedra
transformation cycle takes place inside an inscribing cube of varying edge length, with the 12 vertices always on the surface of the cube. Coxeter, H.S
Kinematics of the cuboctahedron
Kinematics_of_the_cuboctahedron
Solid with 12 equal pentagonal faces
tetrahedra can be inscribed in a cube, and five cubes can be inscribed in a dodecahedron, ten tetrahedra in five cubes can be inscribed in a dodecahedron:
Regular_dodecahedron
Graph with all path lengths between each two vertices
distance in G is at most two) is panconnected. If G is any connected graph, then the cube of G (the graph on the same vertex set that has an edge between
Panconnectivity
Sliding puzzle with fifteen pieces and one space
of the Cube Forum. "5x5 can be solved in 109 MTM". Domain of the Cube Forum. "5x5 sliding puzzle can be solved in 205 moves". Domain of the Cube Forum
15_puzzle
Distance-transitive cubic graph with 20 nodes and 30 edges
has a high level of symmetry, is the only known non-planar cubic partial cube, and has been applied in chemical databases. The name "Desargues graph" has
Desargues_graph
13–14th century kabbalistic text
doctrine from Sefer HaTemunah, of previous Cosmic Shmitah cycles before ours, was that previous cycles refer to spiritual processes, not actual creations; our
Sefer_HaTemunah
Formal linear combination in a cell complex
k-chains are combinations of k-simplices (respectively, k-cubes), but not necessarily connected. Chains are used in homology; the elements of a homology
Chain_(algebraic_topology)
Natural number
the sum of the cubes of the first two non-zero positive integers 1 3 + 2 3 {\displaystyle 1^{3}+2^{3}} which makes it the first cube-sum number greater
9
Polyhedron with 6 faces
sexahedron (pl.: sexahedra or sexahedrons) is any polyhedron with six faces. A cube, for example, is a regular hexahedron with all its faces square, and three
Hexahedron
Topological invariant in mathematics
illustrated by the first of the three graphs for the special case of the cube. (The assumption that the polyhedral surface is homeomorphic to the sphere
Euler_characteristic
disconnected graphs. The set of strong orientations of a graph forms a partial cube, with adjacent orientations in this structure differing in the orientation
Strong_orientation
Rubik's Cube speed solver
solve more than 1000 Rubik's cubes while riding a bicycle. He started SpeedCubing in June 2013 and found out about the World Cube Association (WCA) in December
PK_Arumugam
Cycle graph with all opposite nodes linked
single 4-cycle, while each rung belongs to two such cycles. Therefore, there is no symmetry taking a cycle edge to a rung edge or vice versa. When n ≡ 2 (mod
Möbius_ladder
Graph in which all ordered pairs of linked nodes are automorphic
quasiregular polyhedra: the cube, octahedron, icosahedron, dodecahedron, cuboctahedron, and icosidodecahedron. Extension of the cube to n dimensions gives the
Symmetric_graph
Source code management software
projects and adding team members. New features developed in short development cycles are added to the cloud version first. These features migrate to the on-premises
Azure_DevOps_Server
sequence of truncated cubes joined to each other via opposite octagonal faces form a cycle of 8. Each truncated cube belongs to 3 such cycles. On the other hand
Truncated_24-cells
Describing a family of graphs by excluding certain (sub)graphs
minor Bipartite graphs Odd cycles Subgraph Chordal graphs Cycles of length 4 or more Induced subgraph Perfect graphs Cycles of odd length 5 or more or
Forbidden graph characterization
Forbidden_graph_characterization
Graph divided into two independent sets
one point and every two points be connected with a single line, Levi graphs necessarily do not contain any cycles of length four, so their girth must
Bipartite_graph
Graph with a triangular truncated trapezohedron as its skeleton
of a cube graph, or as the generalized Petersen graph G(6,2). As with any graph of a convex polyhedron, the Dürer graph is a 3-vertex-connected simple
Dürer_graph
self-titled debut album in June. The album, produced by fellow rapper Ice Cube, saw considerable commercial success and went Gold in the US. His prosperity
Mack_10_discography
Solid with twenty equal triangular faces
corners are connected. These rectangular planes can be constructed from a pair of vertices located on the midpoints of the opposite edges on a cube's surface
Regular_icosahedron
Awareness of internal and external existence
consciousness. For example, subjects who stare continuously at a Necker cube usually report that they experience it "flipping" between two 3D configurations
Consciousness
Graph-theoretic description of polyhedra
leaves the rest of G {\displaystyle G} as a connected subgraph. Such cycles are called peripheral cycles. Thus, the combinatorial structure of the faces
Steinitz's_theorem
Nintendo GameCube and Wii emulation software
Dolphin is a free and open-source video game console emulator of the GameCube, Wii and Triforce arcade system that runs on Windows, Linux, macOS, and Android
Dolphin_(emulator)
Shape in hyperbolic geometry
of these shapes, much like the familiar division of Euclidean space into cubes. However, not all polyhedra have ideal versions – a polyhedron can be ideal
Ideal_polyhedron
Flat-sided three-dimensional shape
like the union of two cubes that meet only along a shared edge) and that every vertex is incident to a single alternating cycle of edges and faces (disallowing
Polyhedron
Solid with eight equal triangular faces
a four-connected simplicial well-covered graph. It is also one of the six connected graphs in which the neighborhood of every vertex is a cycle of length
Regular_octahedron
Mathematical version of an order change
are written in cycles. Also, it is common to omit 1-cycles, since these can be inferred: for any element x in S not appearing in any cycle, one implicitly
Permutation
Data storage standard
version simply reduced the number of cycles per bit, with a mark being two cycles of 2400 and a space being one cycle at 1200. It was otherwise the same
Kansas_City_standard
counterexample in many different contexts. Balaban 10-cage Balaban 11-cage Bidiakis cube Brinkmann graph Bull graph Butterfly graph Chvátal graph Diamond graph Dürer
List_of_graphs
Study of graphs defined by geometric means
hyperplane arrangement, can be represented as partial cube graphs. An important special case of a partial cube is the skeleton of the permutohedron, a graph in
Geometric_graph_theory
Archimedean solid with 8 faces
transitive, and has 2 edge orbits of 6 (between triangles) and 12 (on triangle cycles). As a Hamiltonian cubic graph, it can be represented by LCF notation as
Truncated_tetrahedron
-dimensional hypercube (including square and cube). Its distance-two graph is known as the halved cube graph and is the edge graphs of the corresponding
Graph_of_a_polytope
Japanese production continuous improvement process
multiple other lines or processes. Cube kaizen describes the situation where all the points of the planes are connected to each other and no point is disjointed
Kaizen
Type of computer memory
clock cycle. For example, when accessed by a 100 MHz state machine (i.e. a 10 ns clock), the 50 ns DRAM can perform the first read in five clock cycles, and
Dynamic_random-access_memory
1295 = number of edges in the join of two cycle graphs, both of order 35 1296 = 362 = 64, sum of the cubes of the first eight positive integers, the number
1000_(number)
Group of symmetries of an n-dimensional hypercube
{\displaystyle [-3,5,1,-7,2,8,-6,-4]} has three cycles: the negative cycles (1 3) and (4 7 6 8) and the positive cycle (2 5). As a permutation of { − 8 , … , −
Hyperoctahedral_group
2000 Mexican film by Alejandro González Iñárritu
Film Critics Association awards, ahead of cinematic heavyweights such as Cube, Run Lola Run, and Monster's Ball and blockbuster heavyweights such as A
Amores_perros
by the end of its life cycle, being far outpaced by the PS2, which ultimately sold 118 million more units than the GameCube's 21 million. Nintendo stopped
History_of_Nintendo
Suite of development tools
development tools produced for PlayStation 3, PlayStation 2, PSP, Nintendo DS, GameCube, and Game Boy Advance. The phrase PRO-DG was originally registered as a UK
ProDG_(software)
Collection of ideas in music theory
separate major third cycles, all of which exhibit what he formulates as "maximal smoothness." (Cohn, 1996). Another geometric figure, Cube Dance, was invented
Neo-Riemannian_theory
Family of symmetric graphs which generalize the Petersen graph
odd graphs have high odd girth, meaning that they contain long odd-length cycles but no short ones. However their name comes not from this property, but
Odd_graph
Planar graph with quadrilateral faces
vertices. As with median graphs more generally, squaregraphs are also partial cubes: their vertices can be labeled with binary strings such that the Hamming
Squaregraph
Project to demonstrate various space debris removal technologies
a dragsail, and two CubeSats (miniature research satellites). The experiments were as follows: Net experiment - One of the CubeSats, called DebrisSat
RemoveDEBRIS
Cubic graph with 8 vertices and 12 edges
circulant graph in which the vertices can be arranged in a cycle and each vertex is connected to the other vertices whose positions differ by a number that
Wagner_graph
Abstract regular polyhedron with 6 pentagonal faces
regular 4-polytope constructed from 57 hemi-dodecahedra. hemi-icosahedron hemi-cube hemi-octahedron McMullen, Peter; Schulte, Egon (December 2002), "6C. Projective
Hemi-dodecahedron
Hierarchical clustering of graph edges
from graphs to matroids. An unrooted binary tree is a connected undirected graph with no cycles in which each non-leaf node has exactly three neighbors
Branch-decomposition
2002 video game
2002 action-adventure game developed and published by Nintendo for the GameCube. An installment in The Legend of Zelda series, it was released in Japan on
The Legend of Zelda: The Wind Waker
The_Legend_of_Zelda:_The_Wind_Waker
Calculating tool
including addition, subtraction, multiplication, division, and square and cube roots. The beads are first arranged to represent a number, then are manipulated
Abacus
Regular 5-polytope
These constructions can be seen as facets of the 6-orthoplex or rectified 6-cube respectively. A lower symmetry form is a 5-cell pyramid {3,3,3}∨( ), with
5-simplex
Rate of change of acceleration with time
resonance. The graphic captioned "Pole with massive top" shows a block connected to an elastic pole and a massive top. The pole bends when the block accelerates
Jerk_(physics)
Natural number
second-smallest Erdős–Nicolas number, triangular number, number of 5-cubes in a 9-cube, 211 – 25 2017 – Mertens function zero, sexy prime with 2011 2018
2000_(number)
Church in Padua, Veneto, Italy
declared part of the UNESCO World Heritage Site of 14th-century fresco cycles composed of 8 historical buildings in Padua city centre. The Scrovegni Chapel
Scrovegni_Chapel
Embedding a graph in 3D space with no cycles interlinked
in such a way that no two cycles of the graph are linked. A flat embedding is an embedding with the property that every cycle is the boundary of a topological
Linkless_embedding
Natural number
trihexagonal tiling. A regular dodecahedron has twelve pentagonal faces. Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices
12_(number)
Disc-shaped analog sound storage medium
prevent warping. Collectors often store their records in a variety of boxes, cubes, shelves and racks. At the time of the introduction of the compact disc
Phonograph_record
The cycle double cover conjecture: every bridgeless graph has a family of cycles that includes each edge twice The Erdős–Gyárfás conjecture on cycles with
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mass anti-corruption protests
"Serbian students cycle hundreds of miles to take their grievances to the EU". AP News. 15 April 2025. Retrieved 16 April 2025. d. o. o, Cubes (9 April 2025)
2024–present Serbian anti-corruption protests
2024–present_Serbian_anti-corruption_protests
Appliance for cold food storage
Home freezers as separate compartments (larger than necessary just for ice cubes) were introduced in 1940. Frozen foods, previously a luxury item, became
Refrigerator
Video game series
several of Hudson's key designers left to work for Nintendo subsidiary Nd Cube, where they would develop Wii Party. Starting with Mario Party 9 in 2012
Mario_Party
Type of group in abstract algebra
a different point. The order of a cycle is equal to its length. Cycles of length two are transpositions. Two cycles are disjoint if they have disjoint
Symmetric_group
41st season of the reality television series
symbols are in the correct position. Checkpoint #3 (Cube Alignment): Teams must arrange multicolored cubes in a grid to have each color appear once in each
The Challenge: Vets & New Threats
The_Challenge:_Vets_&_New_Threats
French-Canadian former indie video game designer
including SuperHyperCube and Power Pill. Fez was released in April 2012 to widespread acclaim after a protracted five-year development cycle. Its final phases
Phil_Fish
Class of cnidarians distinguished by their cube-shaped medusae
(class Cubozoa) are cnidarian animals distinguished by their box-like (i.e., cube-shaped) body. Some species of box jellyfish produce potent venom delivered
Box_jellyfish
States of matter for water as a solid
molecule remains intact. Because of this, the number of adsorption–desorption cycles ice XVII can withstand is "theoretically infinite". One significant advantage
Phases_of_ice
1992 video game
Retrieved August 30, 2013. "Super Smash Bros. Melee - cube - Walkthrough and Guide - Page 34 - GameSpy". Cube.gamespy.com. January 20, 2002. Archived from the
Kirby's_Dream_Land
Science fantasy book series by Eoin Colfer
fictional C Cube and its recovery. Jon Spiro is an American businessman who has his bodyguard, Arno Blunt, kill Butler and steal Artemis's C Cube, which is
Artemis_Fowl
Voice assistants developed by Amazon
31, 2018). "Huawei joins the Alexa-powered smart speaker club with the AI Cube". CNET. CBS Interactive. Archived from the original on September 1, 2018
Amazon_Alexa
Tactical role-playing video game franchise published by Nintendo
home consoles for Path of Radiance for the GameCube. Despite it arriving late in the GameCube's life cycle, it provided a late boost to sales, reaffirming
Fire_Emblem
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
Boy/Male
Tamil
Collected
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Connected
Boy/Male
Gujarati, Indian
Connected
Boy/Male
American, Australian, British, English, Irish
Rope-maker; A Cape
Surname or Lastname
Scottish and Irish
Scottish and Irish : reduced form of McCure, an Anglicized form of Gaelic Mac Ãomhair (see McIver).English : possibly from Middle English cure ‘charge’, ‘care’, ‘concern’.
Boy/Male
Tamil
Attached, Connected
Boy/Male
Hindu
Attached, Connected
Girl/Female
Hindu
Self connected
Boy/Male
Tamil
Collected
Surname or Lastname
French (Aubé)
French (Aubé) : from the Old French personal name Aube, a variant of Albert. This is a common surname in VT.English (of Norman origin) : nickname from Old French aube, albe ‘white’ (i.e. blond), from Latin albus. Compare Albin.
Male
African
zebra.
Male
English
Pet form of English Reuben, RUBE means "behold, a son!"Â
Boy/Male
German
Bright; Shining Intellect
Boy/Male
English
Ropemaker.
Girl/Female
Tamil
Yuktatma | யà¯à®•à¯à®¤à®¾à®¤à®®à®¾à®‚
Self connected
Yuktatma | யà¯à®•à¯à®¤à®¾à®¤à®®à®¾à®‚
Girl/Female
Australian, Celtic, Irish
Connected to Irish Mythology
Boy/Male
Arabic, Muslim
Joined; Arrived; Connected
Boy/Male
Tamil
Sanyukt | ஸஂயà¯à®•à¯à®¤
Connected, United
Sanyukt | ஸஂயà¯à®•à¯à®¤
Girl/Female
Sikh
Associated, Connected
Boy/Male
Hindu
Connected, United
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
Boy/Male
Hindu
Boy/Male
Indian, Telugu
Lord Hanuman
Boy/Male
Arabic, Hindu, Indian, Muslim
Horseman; Knight
Surname or Lastname
English
English : probably a variant of Letson. This name is found chiefly in TX.
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Devotee of God; Faith; Trust; One Type of Trust
Girl/Female
Indian
Success, Fulfilment, Money and good luck
Girl/Female
Shakespearean
Antony and Cleopatra'. Lady attending on Cleopatra.
Girl/Female
Muslim/Islamic
Acclaim
Girl/Female
French
Victorious.
Girl/Female
Gujarati, Hindu, Indian, Malayalam, Marathi, Telugu
Modest
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
CUBE CONNECTED-CYCLES
n.
Spiritual charge; care of soul; the office of a parish priest or of a curate; hence, that which is committed to the charge of a parish priest or of a curate; a curacy; as, to resign a cure; to obtain a cure.
n.
One who, or that which, connects
n.
The product obtained by taking a number or quantity three times as a factor; as, 4x4=16, and 16x4=64, the cube of 4.
a.
Presenting a combination of a cube and an octahedron.
n.
A flexible tube for connecting the ends of glass tubes in pneumatic experiments.
v. t.
To prepare for preservation or permanent keeping; to preserve, as by drying, salting, etc.; as, to cure beef or fish; to cure hay.
v. t.
To furnish with a tube; as, to tube a well.
n.
Medical or hygienic care; remedial treatment of disease; a method of medical treatment; as, to use the water cure.
v. t.
To form into a cue; to braid; to twist.
imp. & p. p.
of Cube
adv.
In a connected manner.
imp. & p. p.
of Connect
v. i.
To join, unite, or cohere; to have a close relation; as, one line of railroad connects with another; one argument connect with another.
a.
Mutually contrived or planned; agreed on; as, concerted schemes, signals.
a.
Not connected; disconnected.
a.
Separate; unconnected, or imperfectly connected; as, detached parcels.
n.
A priming tube, or friction primer. See under Priming, and Friction.
v. t.
To raise to the third power; to obtain the cube of.
v. i.
To restore health; to effect a cure.
a.
Convicted by one's own consciousness, knowledge, avowal, or acts.