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The term multigraph refers to a graph in which multiple edges between nodes are either permitted (Harary 1994, p. 10; Gross and Yellen 1999, p. 4) or required (Skiena 1990, ...

The necker cube is an illusion in which a two-dimensional drawing of an array of cubes appears to simultaneously protrude from and intrude into the page. A Necker cube ...

In the technical combinatorial sense, an a-ary necklace of length n is a string of n characters, each of a possible types. Rotation is ignored, in the sense that b_1b_2...b_n ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

An Ore graph is a graph that satisfies Ore's theorem, i.e., a graph G for which the sums of the degrees of nonadjacent vertices is greater than or equal to the number of ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...

A parallelian is a line drawn parallel to one side of a triangle. The three lines drawn through a given point are known as the triangle's parallelians. There exists a unique ...

The Penrose triangle, also called the tribar (Cerf), tri-bar (Ernst 1987), impossible tribar (Pappas 1989, p. 13), or impossible triangle, is an impossible figure published ...

The pentagonal icositetrahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal icositetrahedron. It is implemented in the Wolfram Language as ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...