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The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...

A space D is connected if any two points in D can be connected by a curve lying wholly within D. A space is 0-connected (a.k.a. pathwise-connected) if every map from a ...

Graph smoothing, also known as smoothing away or smoothing out, is the process of replacing edges e^'=v_iv_j and e^('')=v_jv_k incident at a vertex v_j of vertex degree 2 by ...

Sequences of integers generated in the Collatz problem. For example, for a starting number of 7, the sequence is 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...

Let Y^X be the set of continuous mappings f:X->Y. Then the topological space Y^X supplied with the compact-open topology is called a mapping space. If (Y,*) is a pointed ...

A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220).

A groupoid S such that for all a,b in S, there exist unique x,y in S such that ax = b (1) ya = b. (2) No other restrictions are applied; thus a quasigroup need not have an ...

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, ...

A pathwise-connected domain is said to be simply connected (also called 1-connected) if any simple closed curve can be shrunk to a point continuously in the set. If the ...

Related to or being the mathematically most simple case. More generally, the word "trivial" is used to describe any result which requires little or no effort to derive or ...