Factors of disconnected graphs and polynomials with nonnegative integer coefficients - Woestijne, Christiaan van de (Ars mathematica contemporanea, 2012)
We investigate the uniqueness of factorisation of possibly disconnected finite graphs with respect to the Cartesian, the strong and the direct product. It is proved that if a graph has ?$n$? connected components, where ?$n$? is prime, or ?$n = 1, 4, 8, 9$?, and satisfies some additional natural conditions, it factors uniquely under the given products. If, on the contrary, ?$n = 6$?$ or 10, all cases of nonunique factorisation are described precisely.
Keywords: factorisation; faktorizacija; graf; graph theory; graphs; monoidi; monoids; teorija grafov