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A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The 24-cell is a finite regular four-dimensional polytope with Schläfli symbol {3,4,3}. It is also known as the hyperdiamond or icositetrachoron, and is composed of 24 ...

The empire problem, also known as the m-pire problem) asks for the maximum number of colors needed to color countries such that no two countries sharing a common border have ...

Given n matches (i.e., rigid unit line segments), find the number of topologically distinct planar arrangements which can be made (Gardner 1991). In this problem, two matches ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

A tree to whose nodes and/or edges labels (usually number) are assigned. The word "weight" also has a more specific meaning when applied to trees, namely the weight of a tree ...

Multiple edges are two or more edges connecting the same two vertices within a multigraph. Multiple edges of degree d_(ij) between vertex i and vertex j correspond to an ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...