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The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

Sexy primes are pairs of primes of the form (p, p+6), so-named since "sex" is the Latin word for "six.". The first few sexy prime pairs are (5, 11), (7, 13), (11, 17), (13, ...

To divide is to perform the operation of division, i.e., to see how many times a divisor d goes into another number n. n divided by d is written n/d or n÷d. The result need ...

Let the multiples m, 2m, ..., [(p-1)/2]m of an integer such that pm be taken. If there are an even number r of least positive residues mod p of these numbers >p/2, then m is ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

One would think that by analogy with the matching-generating polynomial, independence polynomial, etc., a path polynomial whose coefficients are the numbers of paths of ...

Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...