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A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

The edge chromatic number, sometimes also called the chromatic index, of a graph G is fewest number of colors necessary to color each edge of G such that no two edges ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

A nut graph is a graph on n>=2 vertices with adjacency matrix A such that A has matrix rank 1 and contains no 0 element (Sciriha 1998, 2008; Sciriha and Gutman, 1998; and ...

A split graph is a graph whose vertices can be partitioned into a clique and an independent vertex set. Equivalently, it is a chordal graph whose graph complement is also ...

The wedge product is the product in an exterior algebra. If alpha and beta are differential k-forms of degrees p and q, respectively, then alpha ^ beta=(-1)^(pq)beta ^ alpha. ...

For homogeneous polynomials P and Q of degree n, [P,Q]=sum_(i_1,...,i_n>=0)(i_1!...i_n!)(a_(i,...,i_n)b_(i_1,...,i_n)).

A simple graph with n>=3 graph vertices in which each graph vertex has vertex degree >=n/2 has a Hamiltonian cycle.

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

An algebraic surface of degree 9. Enneper's minimal surface is an example of a nonic surface.