Factors of disconnected graphs and polynomials with nonnegative integer coefficients

Christiaan E. van de Woestijne

Abstract


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


graphs, monoids, factorisation

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DOI: https://doi.org/10.26493/1855-3974.202.37f

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications