What question did this study set out to answer?

The aim is to determine how the chromatic number of the Cartesian product of signed graphs is influenced by the chromatic numbers of its factors.

May 17, 2026

The chromatic number of the cartesian product of signed graphs

Puntos clave

The aim is to determine how the chromatic number of the Cartesian product of signed graphs is influenced by the chromatic numbers of its factors.
Analyzed the properties of signed graphs and their Cartesian products.
Established formulas for chromatic numbers based on the parity of the graphs involved.
Demonstrated that the chromatic number of the Cartesian product is determined by the chromatic numbers of its factors.
If one signed graph is even, certain relationships hold between their chromatic numbers.
In cases where a signed graph is odd, graphs exist with specific chromatic number relationships.

Resumen

In 1963, Vizing showed that the chromatic number of the Cartesian product of two graphs is equal to the larger one of the chromatic numbers of these two graphs. This result shows that the chromatic number of the Cartesian product of graphs is determined by its factors’ chromatic numbers. In this paper, we study the chromatic number of the Cartesian product of signed graphs. For signed graphs, we find that the chromatic number of the Cartesian product is also determined by its factors. For any two signed graphs Formula: see text and Formula: see text, we have Formula: see text. Moreover, if Formula: see text is even, then Formula: see text. For the case Formula: see text is odd, there are graphs that satisfy Formula: see text and Formula: see text respectively.

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Cite This Study

Zhou et al. (Fri,) studied this question.

synapsesocial.com/papers/6a095c6d7880e6d24efe29b2 https://doi.org/https://doi.org/10.1142/s1793830926500539

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