Finding the largest graph of given diameter and degree
In graph theory, the degree diameter problem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that the largest degree of any of the vertices in G is at most d. The size of G is bounded above by the Moore bound; for 1 < k and 2 < d only the Petersen graph, the Hoffman-Singleton graph, and possibly graphs (not yet proven to exist) of diameter k = 2 and degree d = 57 attain the Moore bound. In general, the largest degree-diameter graphs are much smaller in size than the Moore bound.
and 23 Related for: Degree diameter problem information
theory, the degreediameterproblem is the problem of finding the largest possible graph G (in terms of the size of its vertex set V) of diameter k such that...
of vertices in any graph with this degree and diameter. Therefore, these graphs solve the degreediameterproblem for their parameters. Another equivalent...
graph theory, the degreediameterproblem is the problem of finding the largest possible graph for a given maximum degree and diameter. The Moore bound...
graphs Conway's 99-graph problem: does there exist a strongly regular graph with parameters (99,14,1,2)? Degreediameterproblem: given two positive integers...
Retrieved 2019-11-11. {{cite book}}: |website= ignored (help) The (Degree, Diameter) Problem for Graphs, Maite71.upc.es, archived from the original on 2012-02-17...
traveller problem Cliques and independent sets Clique problem Connected component Cycle space de Bruijn sequences Degreediameterproblem Entanglement...
Maximum Degree-and-Diameter-Bounded Subgraph problem (MaxDDBS) is a problem in graph theory. Given a connected host graph G, an upper bound for the degree d...
δ {\displaystyle \delta } is the angular diameter in degrees, and d {\displaystyle d} is the actual diameter of the object, and D {\displaystyle D} is...
object of diameter 725.27 km at a distance of one astronomical unit, an object of diameter 45866916 km at one light-year, an object of diameter one astronomical...
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...
of the output torque to the input torque is equal to the ratio of the diameter of the output gear to that of the input gear τout⁄τin = diaout⁄diain. This...
The horizon problem (also known as the homogeneity problem) is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises...
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...
partial differential equation problem. The hp-FEM combines adaptively elements with variable size h and polynomial degree p to achieve exceptionally fast...
following is a list of notable unsolved problems grouped into broad areas of physics. Some of the major unsolved problems in physics are theoretical, meaning...
length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through...
Unsolved problem in computer science: Can the graph isomorphism problem be solved in polynomial time? (more unsolved problems in computer science) The...
research publications, including a widely cited survey of the degreediameterproblem, supervised 20 doctoral students before her death, was the supervisor...
(degree of precision) or the amount of craftsmanship, quality, or cost. They simply refer to the size of the threads relative to the screw diameter. Coarse...
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...
mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae...
Global Information