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The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

A loop of an graph is degenerate edge that joins a vertex to itself, also called a self-loop. A simple graph cannot contain any loops, but a pseudograph can contain both ...

The word "graph" has (at least) two meanings in mathematics. In elementary mathematics, "graph" refers to a function graph or "graph of a function," i.e., a plot. In a ...

A reflexive graph is a pseudograph such that each vertex has an associated graph loop.

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...

The trivial loop is the loop that takes every point to its basepoint. Formally, if X is a topological space and x in X, the trivial loop based at x is the map L:[0,1]->X ...

The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop is an algebraic loop L which, for ...

An algebraic loop L is a Moufang loop if all triples of elements x, y, and z in L satisfy the Moufang identities, i.e., if 1. z(x(zy))=((zx)z)y, 2. x(z(yz))=((xz)y)z, 3. ...

A strange loop is a phenomenon in which, whenever movement is made upwards or downwards through the levels of some hierarchical system, the system unexpectedly arrives back ...

A algebraic loop L is a generalized Bol loop if for all elements x, y, and z of L, ((xy)z)alpha(y)=x((yz)alpha(y)) for some map alpha:L->L. As the name suggests, these are ...