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A planar diagram depicting a link (or knot) as a sequence of segments with gaps representing undercrossings and solid lines overcrossings. In such a diagram, only two ...

A node which is one graph edge further away from a given node in a rooted tree.

An alternating knot is a knot which possesses a knot diagram in which crossings alternate between under- and overpasses. Not all knot diagrams of alternating knots need be ...

A tree with a finite number of branches at each fork and with a finite number of leaves at the end of each branch is called a finitely branching tree. König's lemma states ...

The cross graph is the 6-vertex tree illustrated above. It is implemented in the Wolfram Language as GraphData["CrossGraph"].

Two nodes connected to the same node which are same distance from the root vertex in a rooted tree are called siblings. A function to return the siblings of a vertex v in a ...

A stem-and-leaf diagram, also called a stem-and-leaf plot, is a diagram that quickly summarizes data while maintaining the individual data points. In such a diagram, the ...

An encoding which provides a bijection between the n^(n-2) labeled trees on n nodes and strings of n-2 integers chosen from an alphabet of the numbers 1 to n. A labeled tree ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A labeled graph whose nodes are indexed by the generators of a Coxeter group having (P_i,P_j) as an graph edge labeled by M_(ij) whenever M_(ij)>2, where M_(ij) is an element ...