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The global clustering coefficient C of a graph G is the ratio of the number of closed trails of length 3 to the number of paths of length two in G. Let A be the adjacency ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

Let Q(x)=Q(x_1,x_2,...,x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be ...

The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a nonnegative integer ...

The Laplacian polynomial is the characteristic polynomial of the Laplacian matrix. The second smallest root of the Laplacian polynomial of a graph g (counting multiple values ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

The primes nearest to the nonnegative integers n=0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

A nialpdrome is a number whose hexadecimal digits are in nonincreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 48, 49, ...