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The number of inward directed graph edges from a given graph vertex in a directed graph.

The word "spectrum" confusingly has a number of unrelated meanings in various branches of mathematics.

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The imaginary part I[z] of a complex number z=x+iy is the real number multiplying i, so I[x+iy]=y. In terms of z itself, I[z]=(z-z^_)/(2i), where z^_ is the complex conjugate ...

Sociable numbers are numbers that result in a periodic aliquot sequence, where an aliquot sequence is the sequence of numbers obtained by repeatedly applying the restricted ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

The Komornik-Loreti constant is the value q such that 1=sum_(n=1)^infty(t_k)/(q^k), (1) where {t_k} is the Thue-Morse sequence, i.e., t_k is the parity of the number of 1's ...

Let L denote the partition lattice of the set {1,2,...,n}. The maximum element of L is M={{1,2,...,n}} (1) and the minimum element is m={{1},{2},...,{n}}. (2) Let Z_n denote ...