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The maximum leaf number l(G) of a graph G is the largest number of tree leaves in any of its spanning trees. (The corresponding smallest number of leaves is known as the ...

A McNugget number is a positive integer that can be obtained by adding together orders of McDonald's® Chicken McNuggetsTM (prior to consuming any), which originally came in ...

The network flow problem considers a graph G with a set of sources S and sinks T and for which each edge has an assigned capacity (weight), and then asks to find the maximum ...

The sequence defined by e_0=2 and the quadratic recurrence equation e_n=1+product_(i=0)^(n-1)e_i=e_(n-1)^2-e_(n-1)+1. (1) This sequence arises in Euclid's proof that there ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...

The characteristic polynomial is the polynomial left-hand side of the characteristic equation det(A-lambdaI)=0, (1) where A is a square matrix and I is the identity matrix of ...

A graph is claw-free iff it does not contain the complete bipartite graph K_(1,3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line ...

Let there be n>=2 integers 0<a_1<...<a_n with GCD(a_1,a_2,...,a_n)=1. The values a_i represent the denominations of n different coins, where these denominations have greatest ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...