Search Results for ""

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

The Koch snowflake is a fractal curve, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

A Mersenne number is a number of the form M_n=2^n-1, (1) where n is an integer. The Mersenne numbers consist of all 1s in base-2, and are therefore binary repunits. The first ...

Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

There are several differing definitions of the sun graph. ISGCI defines a (complete) n-sun graph as a graph on 2n nodes (sometimes also known as a trampoline graph; ...

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...