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Let T be a tree defined on a metric over a set of paths such that the distance between paths p and q is 1/n, where n is the number of nodes shared by p and q. Let A be a ...

A set in R^n which can be reduced to one of its points, say P, by a continuous deformation, is said to be contractible. The transformation is such that each point of the set ...

Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius b<a, where a is the radius of a rolling circle. Curtate ...

The distance d(u,v) between two vertices u and v of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path ...

The number of staircase walks on a grid with m horizontal lines and n vertical lines is given by (m+n; m)=((m+n)!)/(m!n!) (Vilenkin 1971, Mohanty 1979, Narayana 1979, Finch ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...

Deck transformations, also called covering transformations, are defined for any cover p:A->X. They act on A by homeomorphisms which preserve the projection p. Deck ...

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

There are two distinct notions of connectivity in a directed graph. A directed graph is weakly connected if there is an undirected path between any pair of vertices, and ...