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The pentatope graph is the skeleton of the pentatope, namely the complete graph K_5. It is sometimes also known as the Kuratowski graph (Nikolić et al. 2000, p. 281). Since ...

A test for the primality of Fermat numbers F_n=2^(2^n)+1, with n>=2 and k>=2. Then the two following conditions are equivalent: 1. F_n is prime and (k/F_n)=-1, where (n/k) is ...

Let C be an error-correcting code consisting of N codewords,in which each codeword consists of n letters taken from an alphabet A of length q, and every two distinct ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

A group that coincides with its commutator subgroup. If G is a non-Abelian group, its commutator subgroup is a normal subgroup other than the trivial group. It follows that ...

A perfect partition is a partition of a number n whose elements uniquely generate any number 1, 2, ..., n. {1,1,...,1_()_(n)} is always a perfect partition of n, and every ...

A perfect ruler also called a complete ruler, is type of ruler considered by Guy (1994) which has k distinct marks spaced such that the distances between marks can be used to ...

The Perko pair is the pair of knots 10_(161) and 10_(162) illustrated above. For many years, they were listed as separate knots in Little (1885) and all similar tables, ...

Let p={a_1,a_2,...,a_n} be a permutation. Then i is a permutation ascent if a_i<a_(i+1). For example, the permutation {1,2,3,4} is composed of three ascents, namely {1,2}, ...

For a permutation alpha in the symmetric group S_p, the alpha-permutation graph of a labeled graph G is the graph union of two disjoint copies of G (say, G_1 and G_2), ...