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1@article{rashidi2020petersen,2  title        = {Computing the zero forcing number for generalized {P}etersen 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 {P}etersen 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 {P}etersen 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 {T}ait colorings with an application to the generalized {P}etersen 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 {P}etersen 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 {C}artesian 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 {P}ython 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 {B}oolean 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
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