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It has been observed that the number of different ways in which a graph with p points can be labelled is p ! divided by the number of symmetries, and that this holds regardless of the species of structure at hand. In this ...

A 1-choice structure arises whenever each person in a group chooses exactly one other person according to some criterion. Our purpose is to study the situation in which these choices are made at random. As noted in Harary, ...

A similarity relation is reflexive and symmetric. A graph may be regarded as a geometric representation of an irreflexive symmetric relation; an r -graph then coincides with a similarity relation. For the realization of ...