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The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS).A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual.
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
The comparability graph for a partially ordered set has a vertex for each set element and an edge between two set elements that are related by the partial order. The order dimension of a partial order is the minimum number of linear orders whose intersection is the given partial order. If a partial order has bounded order dimension, then an ...
Rational numbers are algebraic numbers that satisfy a polynomial of degree 1, while quadratic irrationals are algebraic numbers that satisfy a polynomial of degree 2. For both these sets of numbers we have a way to construct a sequence of natural numbers (a n) with the property that each sequence gives a unique real number and such that this real number belongs to the corresponding set if and ...
Because of the factorization (2n + 1)(n 2 + n + 1), it is impossible for a centered cube number to be a prime number. [3] The only centered cube numbers which are also the square numbers are 1 and 9, [4] [5] which can be shown by solving x 2 = y 3 + 3y, the only integer solutions being (x,y) from {(0,0), (1,2), (3,6), (12,42)}, By substituting a=(x-1)/2 and b=y/2, we obtain x^2=2y^3+3y^2+3y+1.
The Fibonacci cube of order n is the simplex graph of the complement graph of an n-vertex path graph. [2] That is, each vertex in the Fibonacci cube represents a clique in the path complement graph, or equivalently an independent set in the path itself; two Fibonacci cube vertices are adjacent if the cliques or independent sets that they represent differ by the addition or removal of a single ...
For number fields of small degree more refined results are known (Sutherland 2012). A complete list of possible torsion groups has been given for elliptic curves over (see above) and for quadratic and cubic number fields. In degree 1 and 2 all groups that arise occur infinitely often.
1 × 10 ^ 6 m 3 (1,300,000 cu yd; 0.0010 km 3) One cubic hectometre, one gigalitre or one kilostère: 1.4 × 10 6: Volume the 1910 Lakeview Gusher oil spilt (the biggest oil gusher in US history) 1.5644 × 10 6: Volume of concrete in the Panama Canal Locks: 2.6006 × 10 6: Volume of stone in the Great Pyramid of Giza: 3 × 10 6