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arXiv · 1103.0709

Factors of disconnected graphs and polynomials with nonnegative integer coefficients

Christiaan E. van de Woestijne
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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 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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Christiaan E. van de Woestijne. 2011-03-03. Factors of disconnected graphs and polynomials with nonnegative integer coefficients. https://arxiv.org/abs/1103.0709

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