 Alternatively, when some table sizes are repeated, they may be denoted using exponential notation; for instance, formula_3 describes an instance with three tables of size five.Formulated as a problem in graph theory, the pairs of people sitting next to each other at a single meal can be represented as a disjoint union of cycle graphs formula_4 of the specified lengths, with one cycle for each of the dining tables.This union of cycles is a 2-regular graph, and every 2-regular graph has this form.