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Finding the largest graph of given diameter and degree
Unsolved problem in mathematics Given two positive integers d, k, what is the largest graph of diameter k such that all vertices have degrees at most d
Degree_diameter_problem
Regular graph with girth more than twice its diameter
of vertices in any graph with this degree and diameter. Therefore, these graphs solve the degree diameter problem for their parameters. Another equivalent
Moore_graph
graph theory, the degree diameter problem is the problem of finding the largest possible graph for a given maximum degree and diameter. The Moore bound
Table of the largest known graphs of a given diameter and maximal degree
Table_of_the_largest_known_graphs_of_a_given_diameter_and_maximal_degree
Longest distance between two vertices
diameter of a disconnected graph may be defined to be infinite, or undefined. The degree diameter problem seeks tight relations between the diameter,
Diameter_(graph_theory)
vertex transitive digraphs (as of October 2008) in the directed Degree diameter problem are tabulated below. The footnotes in the table indicate the origin
Table of vertex-symmetric digraphs
Table_of_vertex-symmetric_digraphs
99-graph problem: does there exist a strongly regular graph with parameters ( 99 , 14 , 1 , 2 ) {\displaystyle (99,14,1,2)} ? Degree diameter problem: given
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Decentralized distributed system with lookup service
Archived from the original on 2020-03-03. Retrieved 2019-11-11. The (Degree, Diameter) Problem for Graphs, Maite71.upc.es, archived from the original on 2012-02-17
Distributed_hash_table
Length of shortest path between two nodes of a graph
distance Betweenness centrality Centrality Closeness Degree diameter problem for graphs and digraphs Diameter (graph theory) Triameter (graph theory) Metric
Distance_(graph_theory)
The Maximum Degree-and-Diameter-Bounded Subgraph problem (MaxDDBS) is a problem in graph theory. Given a connected host graph G {\displaystyle G} , an
MaxDDBS
How large a sphere or circle appears
δ {\displaystyle \delta } is the angular diameter (in units of angle, normally radians, sometimes in degrees, depending on the arctangent implementation)
Angular_diameter
traveller problem Cliques and independent sets Clique problem Connected component Cycle space de Bruijn sequences Degree diameter problem Entanglement
List_of_graph_theory_topics
Number of cops needed to catch a robber on a graph
shortest path between any two vertices. The Moore bound in the degree diameter problem implies that at least one of these two kinds of guardable sets
Cop_number
Mathematician
is a mathematician specializing in graph theory, including the degree diameter problem and propagation processes on graphs. Originally from Uruguay, and
Daniela_Ferrero
On reflection in a spherical mirror
Alhazen's problem is a mathematical problem in optics concerning reflection in a spherical mirror. It asks for the point in the mirror where one given
Alhazen's_problem
Czech-Australian mathematician and computer scientist
research publications, including a widely cited survey of the degree diameter problem, supervised 20 doctoral students before her death, was the supervisor
Mirka_Miller
Unsolved problem in the mathematics of graph coloring
Cereceda investigated this problem, and found that (even for connected components of the space of colors) the diameter can be exponential for (d + 1)-colorings
Cereceda's_conjecture
Units for measuring angles
symbol ′, is a unit of angular measurement equal to 1/60 of a degree. Since one degree is 1/360 of a turn, or complete rotation, one arcminute is 1/21600
Minute_and_second_of_arc
Mathematics problem
regular graph with n! vertices, its degree is n−1. The pancake sorting problem and the problem to obtain the diameter of the pancake graph are equivalent
Pancake_sorting
Sum of inverse squares of natural numbers
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed
Basel_problem
Cosmological fine-tuning problem
The horizon problem, also known as the homogeneity problem, is a cosmological fine-tuning problem within the Big Bang model of the universe. Observations
Horizon_problem
Number, approximately 3.14
equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of
Pi
System of stars and interstellar matter
estimated distance, leading to an angular diameter (also called "metric diameter"). The isophotal diameter is introduced as a conventional way of measuring
Galaxy
Binary operation in graph theory
with a logarithmic diameter. The power product increases the expansion (hence reduces the diameter) at the price of increasing the degree, and the zigzag
Zig-zag_product
degree diameter problem in graph theory, which seeks the largest possible graph for each combination of degree and diameter. For graphs of diameter two
McKay–Miller–Širáň_graph
Problem in physics and celestial mechanics
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally
N-body_problem
1897 proposed law to define squaring the circle
diameter by one-fourth of the circumference, is not considered a solution to the ancient problem of squaring the circle. This is because the problem is
Indiana_pi_bill
Concept in graph theory
pancakes. Obtaining the pancake number is equivalent to the problem of obtaining the diameter of the pancake graph. The pancake graph of dimension n, Pn
Pancake_graph
Minimum dimension for a vehicle to make a turn
(alternatively, turning diameter or turning circle) of a vehicle defines the minimum dimension (typically the radius or diameter) of available space required
Turning_radius
Fastest curve descent without friction
uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696 and famously solved in one night
Brachistochrone_curve
Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
two values disagree to a high degree of statistical confidence (5.7σ). Are there systematic measurement errors? A problem in the otherwise widely successful
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Shortest network connecting points
tree problem", Journal of Algorithms, 8 (1): 122–130, doi:10.1016/0196-6774(87)90032-0, MR 0875330 Robins, G.; Salowe, J. S. (1995), "Low-degree minimum
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Property of graphs that depends only on abstract structure
a linear combination of the numbers of edges, vertices, and components diameter, the longest of the shortest path lengths between pairs of vertices girth
Graph_property
Centerfire rifle cartridge
aerodynamic efficiency and external ballistic performance for the projectile diameter. For some loads, the 6.5mm Creedmoor is capable of duplicating the muzzle
6.5mm_Creedmoor
Simple curve of Euclidean geometry
two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been
Circle
Unsolved problem in computational complexity theory
Unsolved problem in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph
Graph_isomorphism_problem
Problems which attempt to find the most efficient way to pack objects into containers
The rectangular cuboids to be packed can be rotated by 90 degrees on each axis. The problem of finding the smallest ball such that k disjoint open unit
Packing_problems
Rifle cartridge designed by the U.S. Army
expected of infantry fire. While the nominal bore diameter was .450 inches (11.4 mm), the groove diameter was actually closer to .458 inches (11.6 mm). As
.45-70
Academic field
path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing problem, critical
Network_science
Problem in object-oriented programming
The circle–ellipse problem in software development (sometimes called the square–rectangle problem) illustrates several pitfalls which can arise when using
Circle–ellipse_problem
Graph without triples of adjacent vertices
chromatic number and minimum degree (1/3 − ε)n for any ε > 0. Andrásfai graph, a family of triangle-free circulant graphs with diameter two Henson graph, an infinite
Triangle-free_graph
Number of vertices with unambiguous distances
the vertices in S. Finding the metric dimension of a graph is an NP-hard problem; the decision version, determining whether the metric dimension is less
Metric dimension (graph theory)
Metric_dimension_(graph_theory)
Node labeling problem in graph theory
In graph theory, the graph bandwidth problem may be visualized as placing the vertices of a given graph at distinct integer positions along the number
Graph_bandwidth
Cubic graph with 10 vertices and 15 edges
Unsolved problem in mathematics Conjecture: Every bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics
Petersen_graph
Numerical method for solving physical or engineering problems
partial differential equation problem. The hp-FEM combines adaptively elements with variable size h and polynomial degree p to achieve exceptionally fast
Finite_element_method
Machine used to grind or blend materials
rubber lined mills. The length of the mill is approximately equal to its diameter. The general idea behind the ball mill is an ancient one, but it was not
Ball_mill
Concept in geometry
represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which
Area_of_a_circle
Astronomical observatory in Chile
variant of three-mirror anastigmat to deliver sharp images over a 3.5-degree-diameter field of view. Images are recorded by a 3.2-gigapixel charge-coupled
Vera_C._Rubin_Observatory
Brand of tea and juice drinks
million for himself and his investors from the sale. Quaker Oats ran into problems and sold Snapple to Triarc in 1997 for $300 million. In September 2000
Snapple
Geometric construction
as its diameter a chord spanning a right angle on the larger circle. Equivalently, it is a non-convex plane region bounded by one 180-degree circular
Lune_of_Hippocrates
Swiss/Finnish rifle cartridge
Reduced barrel wear compared to 6mm Norma BR The 6.5×47mm Lapua has a base diameter and overall length similar to the 7.62×51mm NATO/.308 Winchester, allowing
6.5×47mm_Lapua
Grooves in a weapon barrel for accuracy
needed to gyroscopically stabilize it: barrels intended for short, large-diameter projectiles such as spherical lead balls require a very low twist rate
Rifling
Rifle cartridge
reduced the diameter of the lands and grooves whilst leaving the Patrone 88 cartridge itself unchanged. These efforts solved the problems the German military
Patrone_88
Polynomial equation of degree 3
(This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem
Cubic_equation
Number denoting a graph's closeness to a tree
particular this is trivially true for a class of bounded degree graphs, as bounded diameter subgraphs have bounded size. Another example is given by 1-planar
Treewidth
Non-standard rifle cartridge
for that sport. The 226 Express subvariant, reduces shoulder and neck diameter with a long, slender body taper on the 30-06 case. Experimentation during
.30-06 Springfield wildcat cartridges
.30-06_Springfield_wildcat_cartridges
Single, usually cylindrical, flexible strand or bar or rod of metal
and so producing wire of incorrect diameter. Diamond dies must be re-bored when they have lost their original diameter of hole, but metal dies are brought
Wire
Holocene climate period during which northern Africa was wetter than today
other; in general, the simulation of the Green Sahara is considered a problem for Earth system models. There is more evidence of the late phase of the
African_humid_period
Type of shaped charge explosive
spin-stabilization, another problem with any barreled weapon (that is, a gun) is that a large-diameter shell has worse accuracy than a small-diameter shell of the same
High-explosive_anti-tank
Species of slime mold, model organism
available, the network-shaped plasmodium can grow to a foot or more in diameter. Like amoebae, the plasmodium can consume whole microbes, but also readily
Physarum_polycephalum
Helical structure used to convert between rotational and linear movement or force
fasteners to fail. The minor diameter is the lower extreme diameter of the thread. Major diameter minus minor diameter, divided by two, equals the height
Screw_thread
by adding 1. The two problems are essentially differ only by notation in most regards, and so are often considered the same problem. The name "radio coloring"
Radio_coloring
Type of pump
Tube inner diameter – higher flow rate with larger inner diameter. Pump-head outer diameter – higher flow rate with larger outer diameter. Pump-head rotational
Peristaltic_pump
Theorem on polygon dissections
σ(P,Q). For instance, Alfred Tarski proved that if P is convex and the diameters of P and Q are respectively given by d(P) and d(Q), then σ ( P , Q ) ≥
Wallace–Bolyai–Gerwien theorem
Wallace–Bolyai–Gerwien_theorem
Rotating circular machine part with teeth that mesh with another toothed part
materials, and are used for many different functions and applications. Diameters may range from a few μm in micromachines, to a few mm in watches and toys
Gear
Swiss mathematician (1707–1783)
(lowercase pi) to denote the ratio of a circle's circumference to its diameter, as well as first using the notation f ( x ) {\displaystyle f(x)} for the
Leonhard_Euler
Disc-shaped analog sound storage medium
the 2010s and 2020s. Phonograph records are generally described by their diameter in inches (12-inch, 10-inch, 7-inch), the rotational speed in revolutions
Phonograph_record
Measurement of the human penis
Cohen, Philip R. (1 February 2021). "Adult Acquired Buried Penis: A Hidden Problem in Obese Men". Cureus. 13 (2) e13067. doi:10.7759/cureus.13067. PMC 7932830
Human_penis_size
American theoretical physicist and cosmologist
about 300,000 years after the Big Bang, the observable universe had a diameter of 90 million light-years. There was no time for one end of the cosmos
Alan_Guth
Unit of temperature
This led him to be elected a fellow of the Royal Society. A 0.5-inch-diameter cylinder made from pipe clay was dried at the temperature of boiling water
Wedgwood_scale
Physiological phenomenon involving the hardening and enlargement of the penis
centimetres (20 in) long and 2.5 to 6 centimetres (0.98 to 2.36 in) in diameter with the distal end 15 to 20 centimetres (5.9 to 7.9 in). The retractor
Erection
The Moon's circuit around Earth
290 mph), the Moon covers a distance of approximately its diameter, or about half a degree on the celestial sphere, each hour. The Moon differs from most
Orbit_of_the_Moon
Plane figure bounded by line segments
sides meet at right angles, i.e. all its interior angles are 90 or 270 degrees. Monotone with respect to a given line L: every line orthogonal to L intersects
Polygon
Comparison of a wide range of lengths
20 km – diameter of Leda, one of Jupiter's moons 20 km – diameter of Pan, one of Saturn's moons 20 km – diameter of the Crab Pulsar. 22 km – diameter of Phobos
Orders_of_magnitude_(length)
Firearms cartridge
this problem by using the external dimensions and lead angle as found in the military 5.56×45mm NATO cartridge and the 0.224 inch freebore diameter as found
.223_Remington
Graph drawn with all edges intersecting
biggest little polygon problem, of finding an n {\displaystyle n} -gon with maximum area relative to its diameter. Unsolved problem in mathematics Can a
Thrackle
American convicted murderer; last person to be hanged in the US
of manslaughter instead of first degree murder. She pointed to Bailey's upbringing, his worsening drinking problems stemmed from recent events involving
Billy_Bailey
Human male external reproductive organ
are small, raised, yellowish-white spots 1–2 mm (roughly 0.05 inch) in diameter that may appear on the penis, which again are common and not infectious
Human_penis
Aircraft component
aircraft in the early 1910s, originally to reduce drag caused by the large-diameter rotary engines of that era, and also were prominent on World War I-era
Spinner_(aeronautics)
Series of V8 engines built by Chrysler
a strong flame front. However, if the hemi-head hemisphere is of equal diameter to the piston, there is minimal squish for proper turbulence to mix fuel
Chrysler_Hemi_engine
Species of bird
above the ground, and in trees usually of 21 to 52 cm (8.3 to 20.5 in) in diameter. Usually nest sites are within plots of woodland of at least 4 to 8 ha
Cooper's_hawk
American electric vehicle and clean energy company
the first generation Roadster, it used off-the-shelf 18650-type (18 mm diameter, 65 mm height) cylindrical batteries that were already used for other consumer
Tesla,_Inc.
Murder of young American girl
left elbow, as well as injuries to her genital area consistent with the diameter of a rolling pin handle. A bloodstained piece of cloth was found tied in
Murder_of_Sandra_Cantu
Rimless, centerfire, bottlenecked rifle cartridge
Winchester .338 Federal .358 Winchester .30 Remington AR 7mm caliber Delta L problem List of firearms List of rifle cartridges Sectional density Table of handgun
.308_Winchester
Range of physical processes in physics
factors including polarization, angle, and coherence. For larger diameters, the problem of electromagnetic scattering by spheres was first solved by Gustav
Scattering
Hypothetical invisible cosmic material
Unsolved problem in physics What is dark matter? How was it generated? More unsolved problems in physics In astronomy and cosmology, dark matter is an
Dark_matter
Concept in graph theory
graph G is strongly regular with μ > 0, then G is distance-regular with diameter 2. Likewise, if G is strongly regular with λ = 1, then it is locally linear
Strongly_regular_graph
Reciprocating internal combustion engine
System — intelligent/DBW), PA6 plastic intake, and increased throttle body diameter over the 1MZ. The 3MZ uses a new flat-type knock sensor, which is a departure
Toyota_MZ_engine
Tool used to measure dimensions of an object
dimensions of an object or hole; namely, the length, width, thickness, diameter or depth of an object or hole. The word caliper comes from a corrupt form
Calipers
Species of jellyfish
It can grow up to 10 kg of weight, and its bell is commonly 40–60 cm in diameter, but can be up to 90 cm. The European Union lists it as one of the worst
Rhopilema_nomadica
wooden or metal rod used to hit the ball thrown by the pitcher. A bat's diameter is larger at one end (the barrel-end) than at the other (the handle). The
Glossary_of_baseball_terms
Current global map of airborne particulates less than 1 micrometer in diameter, including smoke, centered on Australia MyFireWatch – Government of Western
2019–20 Australian bushfire season
2019–20_Australian_bushfire_season
Decreased ability to see
corrected to better than 20/200 in the better eye, or who has 20 degrees (diameter) or less of visual field remaining, is considered legally blind or
Visual_impairment
Unit of length in astronomy
distance from which a disc that is one au in diameter must be viewed for it to have an angular diameter of one arcsecond (by placing the observer at D
Parsec
Triangle containing a 90-degree angle
its right-triangular half is scalene. Every triangle whose base is the diameter of a circle and whose apex lies on the circle is a right triangle, with
Right_triangle
Branch of mathematics
algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern
Algebraic_geometry
Outermost layer of the Sun's atmosphere
visible limb is on the order of 10−6 and decreases to 10−9 within a solar diameter from the limb. Furthermore, the sky brightness can be more than three to
Solar_corona
Scientific projections regarding the far future
"Sinks in the landscape, Boltzmann brains and the cosmological constant problem". Journal of Cosmology and Astroparticle Physics. 2007 (1): 022. arXiv:hep-th/0611043
Timeline_of_the_far_future
Speakers of Austronesian languages
during conflicts. The house posts are also distinctively capped with larger-diameter discs at the top, to prevent vermin and pests from entering the structures
Austronesian_peoples
Coastal defense ship class of the German Imperial Navy
loss. In the late 1880s, the German Kaiserliche Marine grappled with the problem of what type of capital ship to build in the face of limited naval budgets
Odin-class coastal defense ship
Odin-class_coastal_defense_ship
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