Factors of disconnected graphs and polynomials with nonnegative integer coefficients

Details Factors of disconnected graphs and polynomials with nonnegative integer coefficients Factors of disconnected graphs and polynomials with nonnegative integer coefficients

2011-03-03

arxiv.org/abs/1103.0709v1

Mathematics

Combinatorics

14 pages

Scientific paper

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 conditions, it factors uniquely under the given products. If, on the contrary, $n=6$ or 10, all cases of nonunique factorisation are described precisely.

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