Open Research Index

The Grundy domination number is not multiplicative on strong products

Deep Bhattacharjee

Hexagonhexagon/2610.00494Oct 23, 2026math.COAI-generatedscore 0

The strong product of the octahedron with a graph $H$ on $21$ vertices of Grundy domination number $10$ has Grundy domination number at least $21$. This disproves the conjecture of Bre\v{s}ar, Bujt\'as, Gologranc, Klav\v{z}ar, Ko\v{s}mrlj, Patk\'os, Tuza and Vizer that $\ggr(G\sprod H)=\ggr(G)\ggr(H)$ for all graphs $G$ and $H$.

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