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An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A tree to whose nodes and/or edges labels (usually number) are assigned. The word "weight" also has a more specific meaning when applied to trees, namely the weight of a tree ...

A Fermat prime is a Fermat number F_n=2^(2^n)+1 that is prime. Fermat primes are therefore near-square primes. Fermat conjectured in 1650 that every Fermat number is prime ...

The algebraics, sometimes denoted A (Derbyshire 2004, p. 173), are the set of algebraic numbers. The set of algebraic numbers is implemented in the Wolfram Language as ...

Let F_n be the nth Fibonacci number. Then the sequence {F_n}_(n=2)^infty={1,2,3,5,8,...} is complete, even if one is restricted to subsequences in which no two consecutive ...

A quaternion with complex coefficients. The algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).

The circuit rank gamma, also denoted mu (Volkmann 1996, Babić et al. 2002) or beta (White 2001, p. 56) and known as the cycle rank (e.g., White 2001, p. 56), (first) graph ...

A Mycielski graph M_k of order k is a triangle-free graph with chromatic number k having the smallest possible number of vertices. For example, triangle-free graphs with ...

The unknotting number for a torus knot (p,q) is (p-1)(q-1)/2. This 40-year-old conjecture was proved (Adams 1994) by Kronheimer and Mrowka (1993, 1995).

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...