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A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

Two lines PQ and RS are said to be antiparallel with respect to the sides of an angle A if they make the same angle in the opposite senses with the bisector of that angle. If ...

An automorphic graph is a distance-transitive graph Gamma for which the automorphism group Aut(Gamma) acts primitively on the vertices of Gamma and is not a complete graph or ...

B-trees were introduced by Bayer (1972) and McCreight. They are a special m-ary balanced tree used in databases because their structure allows records to be inserted, ...

The curlicue fractal is a figure obtained by the following procedure. Let s be an irrational number. Begin with a line segment of unit length, which makes an angle phi_0=0 to ...

A cycle of a graph G, also called a circuit if the first vertex is not specified, is a subset of the edge set of G that forms a path such that the first node of the path ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...

An isolated point of a graph is a node of degree 0 (Hartsfield and Ringel 1990, p. 8; Harary 1994, p. 15; D'Angelo and West 2000, p. 212; West 2000, p. 22). The number of ...

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, ...