Geodesic
Factors of disconnected graphs and polynomials with nonnegative integer coefficients
Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 307-323.

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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.
DOI : 10.26493/1855-3974.202.37f
Keywords: graphs, monoids, factorisation 
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Christiaan E. van de Woestijne. Factors of disconnected graphs and polynomials with nonnegative integer coefficients. Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 307-323. doi : 10.26493/1855-3974.202.37f. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.202.37f/

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