Year: 2026
Type: preprint
Abstract: We determine the Grundy total domination number and the skew zero forcing number for every Cartesian product of two paths or cycles, thereby closing the nonmatching bounds previously known for these rectangular, cylindrical, and toroidal families. For $2\le a\le b$, \[ Z_-(P_a\square P_b) =a-\mathbf1_{\{a\ {\rm odd},\,b\ {\rm even}\}}. \] For $p\ge2$ and $c\ge3$, \[ Z_-(P_p\square C_c)= \begin{cases} \min\{p,c\},&c\text{ is odd}, \min\{2p,c\},&c\text{ is even}. \end{cases} \] Finally, for $3\le a\le b$, \[ Z_-(C_a\square C_b)= \begin{cases} 2a-1,&a=b\text{ odd}, 2a,&a=b\text{ even}, \min\{b,2a\},&a
Source: arXiv (Cornell University)
Author: Chang, Fei-Huang
Institution: National Dong Hwa University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204836298