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A graph with a finite number of nodes and edges. If it has n nodes and has no multiple edges or graph loops (i.e., it is simple), it is a subgraph of the complete graph K_n. ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

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 ...

The Ljubljana graph is a graph on 112 vertices that is the third smallest cubic semisymmetric graph. It was discovered by Brouwer et al. (1993) and rediscovered by Conder et ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...

When P and Q are integers such that D=P^2-4Q!=0, define the Lucas sequence {U_k} by U_k=(a^k-b^k)/(a-b) for k>=0, with a and b the two roots of x^2-Px+Q=0. Then define a ...

A macron is a bar placed over a single symbol or character, such as x^_. The symbol z^_ is sometimes used to denote the following operations: 1. The complex conjugate z^_. 2. ...

A modular inverse of an integer b (modulo m) is the integer b^(-1) such that bb^(-1)=1 (mod m). A modular inverse can be computed in the Wolfram Language using PowerMod[b, ...

The word multiplicity is a general term meaning "the number of values for which a given condition holds." For example, the term is used to refer to the value of the totient ...