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A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

A problem posed by L. Collatz in 1937, also called the 3x+1 mapping, 3n+1 problem, Hasse's algorithm, Kakutani's problem, Syracuse algorithm, Syracuse problem, Thwaites ...

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n(n-1)/2 (the ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

Start with an integer n, known as the digitaddition generator. Add the sum of the digitaddition generator's digits to obtain the digitaddition n^'. A number can have more ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

A graph G is distance transitive if its automorphism group is transitive on pairs of vertices at each pairwise distance in the graph. Distance-transitivity is a ...

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 ...

The dodecahedral graph is the Platonic graph corresponding to the connectivity of the vertices of a dodecahedron, illustrated above in four embeddings. The left embedding ...