1@article{rashidi2020petersen,2 title = {Computing the zero forcing number for generalized Petersen graphs},3 author = {Rashidi, Saeedeh and Poursalavati, Nosratollah Shajareh and Tavakkoli, Maryam},4 journal = {Journal of Algebra Combinatorics Discrete Structures and Applications},5 year = {2020},6 volume = {7},7 number = {2},8 pages = {183-193},9 publisher = {iPeak Academy Ltd.},10 doi = {10.13069/jacodesmath.729465},11 url = {https://doi.org/10.13069/jacodesmath.729465},12}13@article{aim2008zeroforcing,14 title = {Zero forcing sets and the minimum rank of graphs},15 author = {AIM Minimum Rank – Special Graphs Work Group},16 journal = {Linear Algebra and its Applications},17 year = {2008},18 volume = {428},19 number = {7},20 pages = {1628-1648},21 publisher = {Elsevier BV},22 doi = {10.1016/j.laa.2007.10.009},23 url = {https://doi.org/10.1016/j.laa.2007.10.009},24}25@article{arxiv2610_24059,26 title = {Sharp zero forcing numbers for the generalized Petersen graphs $P(n,3)$ and $P(n,4)$},27 author = {Arnav Krishnan and Haobo Ma and Wenlin Zhang},28 journal = {arXiv preprint arXiv:2610.24059},29 year = {2026},30 eprint = {2610.24059},31 archivePrefix = {arXiv},32 primaryClass = {math.CO},33 url = {https://arxiv.org/abs/2610.24059},34}35@article{arxiv2607_19412,36 title = {A correction to the Zero Forcing Number of the Generalized Petersen Graphs $P(n,3)$},37 author = {Arnav Krishnan},38 journal = {arXiv preprint arXiv:2607.19412},39 year = {2026},40 eprint = {2607.19412},41 archivePrefix = {arXiv},42 primaryClass = {math.CO},43 url = {https://arxiv.org/abs/2607.19412},44}45@article{brimkov2019computational,46 title = {Computational approaches for zero forcing and related problems},47 author = {Brimkov, Boris and Fast, Caleb C. and Hicks, Illya V.},48 journal = {European Journal of Operational Research},49 year = {2019},50 volume = {273},51 number = {3},52 pages = {889-903},53 publisher = {Elsevier BV},54 doi = {10.1016/j.ejor.2018.09.030},55 url = {https://doi.org/10.1016/j.ejor.2018.09.030},56}57@article{brimkov2021improved,58 title = {Improved Computational Approaches and Heuristics for Zero Forcing},59 author = {Brimkov, Boris and Mikesell, Derek and Hicks, Illya V.},60 journal = {INFORMS Journal on Computing},61 year = {2021},62 publisher = {Institute for Operations Research and the Management Sciences (INFORMS)},63 doi = {10.1287/ijoc.2020.1032},64 url = {https://doi.org/10.1287/ijoc.2020.1032},65}66@article{alameda2018families,67 title = {Families of graphs with maximum nullity equal to zero forcing number},68 author = {Alameda, Joseph S. and Curl, Emelie and Grez, Armando and Hogben, Leslie and Kingston, O’Neill and Schulte, Alex and Young, Derek and Young, Michael},69 journal = {Special Matrices},70 year = {2018},71 volume = {6},72 number = {1},73 pages = {56-67},74 publisher = {Walter de Gruyter GmbH},75 doi = {10.1515/spma-2018-0006},76 url = {https://doi.org/10.1515/spma-2018-0006},77}78@article{watkins1969tait,79 title = {A theorem on tait colorings with an application to the generalized Petersen graphs},80 author = {Watkins, Mark E.},81 journal = {Journal of Combinatorial Theory},82 year = {1969},83 volume = {6},84 number = {2},85 pages = {152-164},86 publisher = {Elsevier BV},87 doi = {10.1016/s0021-9800(69)80116-x},88 url = {https://doi.org/10.1016/s0021-9800(69)80116-x},89}90@article{frucht1971groups,91 title = {The groups of the generalized Petersen graphs},92 author = {Frucht, Roberto and Graver, Jack E. and Watkins, Mark E.},93 journal = {Mathematical Proceedings of the Cambridge Philosophical Society},94 year = {1971},95 volume = {70},96 number = {2},97 pages = {211-218},98 publisher = {Cambridge University Press (CUP)},99 doi = {10.1017/s0305004100049811},100 url = {https://doi.org/10.1017/s0305004100049811},101}102@incollection{wetzler2014drattrim,103 title = {DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs},104 author = {Wetzler, Nathan and Heule, Marijn J. H. and Hunt, Warren A.},105 booktitle = {Lecture Notes in Computer Science},106 year = {2014},107 pages = {422-429},108 publisher = {Springer International Publishing},109 doi = {10.1007/978-3-319-09284-3\_31},110 url = {https://doi.org/10.1007/978-3-319-09284-3\_31},111}112@article{cameron2023forts,113 title = {Forts, (fractional) zero forcing, and Cartesian products of graphs},114 author = {Thomas R. Cameron and Leslie Hogben and Franklin H. J. Kenter and Seyed Ahmad Mojallal and Houston Schuerger},115 journal = {arXiv preprint arXiv:2310.17904},116 year = {2023},117 eprint = {2310.17904},118 archivePrefix = {arXiv},119 primaryClass = {math.CO},120 url = {https://arxiv.org/abs/2310.17904},121}122@article{davila2015girth,123 title = {Bounds for the Zero Forcing Number of Graphs with Large Girth},124 author = {Davila, Randy and Kenter, Franklin},125 journal = {Theory and Applications of Graphs},126 year = {2015},127 volume = {2},128 number = {2},129 publisher = {Georgia Southern University},130 doi = {10.20429/tag.2015.020201},131 url = {https://doi.org/10.20429/tag.2015.020201},132}133@article{hogben2012propagation,134 title = {Propagation time for zero forcing on a graph},135 author = {Hogben, Leslie and Huynh, My and Kingsley, Nicole and Meyer, Sarah and Walker, Shanise and Young, Michael},136 journal = {Discrete Applied Mathematics},137 year = {2012},138 volume = {160},139 number = {13-14},140 pages = {1994-2005},141 publisher = {Elsevier BV},142 doi = {10.1016/j.dam.2012.04.003},143 url = {https://doi.org/10.1016/j.dam.2012.04.003},144}145@article{bjorkman2025leaky,146 title = {Leaky Forcing: Extending Zero Forcing Results to a Fault-Tolerant Setting},147 author = {Beth Bjorkman and Lei Cao and Franklin Kenter and Ryan Moruzzi and Carolyn Reinhart and Violeta Vasilevska},148 journal = {arXiv preprint arXiv:2508.02564},149 year = {2025},150 eprint = {2508.02564},151 archivePrefix = {arXiv},152 primaryClass = {math.CO},153 url = {https://arxiv.org/abs/2508.02564},154}155@article{fast2018degrees,156 title = {Effects of vertex degrees on the zero-forcing number and propagation time of a graph},157 author = {Fast, Caleb C. and Hicks, Illya V.},158 journal = {Discrete Applied Mathematics},159 year = {2018},160 volume = {250},161 pages = {215-226},162 publisher = {Elsevier BV},163 doi = {10.1016/j.dam.2018.05.002},164 url = {https://doi.org/10.1016/j.dam.2018.05.002},165}166@article{barioli2010parameters,167 title = {Zero forcing parameters and minimum rank problems},168 author = {Barioli, Francesco and Barrett, Wayne and Fallat, Shaun M. and Hall, H. Tracy and Hogben, Leslie and Shader, Bryan and van den Driessche, P. and van der Holst, Hein},169 journal = {Linear Algebra and its Applications},170 year = {2010},171 volume = {433},172 number = {2},173 pages = {401-411},174 publisher = {Elsevier BV},175 doi = {10.1016/j.laa.2010.03.008},176 url = {https://doi.org/10.1016/j.laa.2010.03.008},177}178@incollection{ignatiev2018pysat,179 title = {PySAT: A Python Toolkit for Prototyping with SAT Oracles},180 author = {Ignatiev, Alexey and Morgado, Antonio and Marques-Silva, Joao},181 booktitle = {Lecture Notes in Computer Science},182 year = {2018},183 pages = {428-437},184 publisher = {Springer International Publishing},185 doi = {10.1007/978-3-319-94144-8\_26},186 url = {https://doi.org/10.1007/978-3-319-94144-8\_26},187}188@incollection{demoura2021lean4,189 title = {The Lean 4 Theorem Prover and Programming Language},190 author = {Moura, Leonardo de and Ullrich, Sebastian},191 booktitle = {Lecture Notes in Computer Science},192 year = {2021},193 pages = {625-635},194 publisher = {Springer International Publishing},195 doi = {10.1007/978-3-030-79876-5\_37},196 url = {https://doi.org/10.1007/978-3-030-79876-5\_37},197}198@incollection{sinz2005cardinality,199 title = {Towards an Optimal CNF Encoding of Boolean Cardinality Constraints},200 author = {Sinz, Carsten},201 booktitle = {Lecture Notes in Computer Science},202 year = {2005},203 pages = {827-831},204 publisher = {Springer Berlin Heidelberg},205 doi = {10.1007/11564751\_73},206 url = {https://doi.org/10.1007/11564751\_73},207}208@article{hogben2022book,209 title = {Inverse Problems and Zero Forcing for Graphs},210 author = {Hogben, Leslie and Lin, Jephian and Shader, Bryan},211 journal = {Mathematical Surveys and Monographs},212 year = {2022},213 publisher = {American Mathematical Society},214 doi = {10.1090/surv/270},215 url = {https://doi.org/10.1090/surv/270},216}217