1{2 "sources": [3 {4 "key": "rashidi2020petersen",5 "kind": "doi",6 "identifier": "10.13069/jacodesmath.729465",7 "title": "Computing the zero forcing number for generalized Petersen graphs",8 "authors": [9 "Rashidi, Saeedeh",10 "Poursalavati, Nosratollah Shajareh",11 "Tavakkoli, Maryam"12 ],13 "year": 2020,14 "venue": "Journal of Algebra Combinatorics Discrete Structures and Applications",15 "url": "https://doi.org/10.13069/jacodesmath.729465",16 "verified": true,17 "verifiedAt": "2026-10-30T17:22:32.307Z",18 "verificationMethod": "crossref",19 "accessLevel": "full-text",20 "notes": "Full text read (open-access PDF, CC BY 4.0, saved at sources/fulltext/rashidi2020.pdf). Thm 2.1: n=rk+s => Z<=r(s+2); Thm 2.2: Z<=2k+2; Thm 2.6: Z(P(2k+1,k))=6 for k>=5; Remark 2.4 attributes Z(P(24r,5))=12 to Alameda et al.; Cor 3.5 lower bound min{k,floor(n/k)}+1. Thm 3.6 (k=3) is known to be false at n=12.",21 "claimedTitle": "Computing the zero forcing number for generalized Petersen graphs",22 "titleSimilarity": 123 },24 {25 "key": "aim2008zeroforcing",26 "kind": "doi",27 "identifier": "10.1016/j.laa.2007.10.009",28 "title": "Zero forcing sets and the minimum rank of graphs",29 "authors": [30 "AIM Minimum Rank – Special Graphs Work Group"31 ],32 "year": 2008,33 "venue": "Linear Algebra and its Applications",34 "url": "https://doi.org/10.1016/j.laa.2007.10.009",35 "verified": true,36 "verifiedAt": "2026-10-30T17:16:23.957Z",37 "verificationMethod": "crossref",38 "accessLevel": "metadata",39 "claimedTitle": "Zero forcing sets and the minimum rank of graphs",40 "titleSimilarity": 141 },42 {43 "key": "arxiv2610_24059",44 "kind": "arxiv",45 "identifier": "2610.24059",46 "title": "Sharp zero forcing numbers for the generalized Petersen graphs $P(n,3)$ and $P(n,4)$",47 "authors": [48 "Arnav Krishnan",49 "Haobo Ma",50 "Wenlin Zhang"51 ],52 "year": 2026,53 "venue": "arXiv",54 "url": "https://arxiv.org/abs/2610.24059",55 "verified": true,56 "verifiedAt": "2026-10-30T17:22:39.119Z",57 "verificationMethod": "arxiv-api",58 "accessLevel": "full-text",59 "notes": "Full text read (arXiv HTML + PDF saved at sources/fulltext/arxiv_2610.24059.pdf). Z(P(n,3))=8 for n>=13, Z(P(n,4))=10 for n>=18, thresholds sharp; lower bounds by boundary of first forcing sources + column deletion + forts; Lean 4 for k=3, DRAT for k=4. Contains no statement about k=5.",60 "claimedTitle": "Sharp zero forcing numbers for the generalized Petersen graphs P(n,3) and P(n,4)",61 "titleSimilarity": 162 },63 {64 "key": "arxiv2607_19412",65 "kind": "arxiv",66 "identifier": "2607.19412",67 "title": "A correction to the Zero Forcing Number of the Generalized Petersen Graphs $P(n,3)$",68 "authors": [69 "Arnav Krishnan"70 ],71 "year": 2026,72 "venue": "arXiv",73 "url": "https://arxiv.org/abs/2607.19412",74 "verified": true,75 "verifiedAt": "2026-10-30T17:22:39.147Z",76 "verificationMethod": "arxiv-api",77 "accessLevel": "full-text",78 "notes": "Full text read (arXiv HTML + PDF saved at sources/fulltext/arxiv_2607.19412.pdf). Z(P(12,3))=7 corrects Rashidi Thm 3.6; table 7<=n<=20; states exhaustive search confirms Z(P(11,5))=6; k>=4 stabilization thresholds left open.",79 "claimedTitle": "A correction to the Zero Forcing Number of the Generalized Petersen Graphs P(n,3)",80 "titleSimilarity": 181 },82 {83 "key": "brimkov2019computational",84 "kind": "doi",85 "identifier": "10.1016/j.ejor.2018.09.030",86 "title": "Computational approaches for zero forcing and related problems",87 "authors": [88 "Brimkov, Boris",89 "Fast, Caleb C.",90 "Hicks, Illya V."91 ],92 "year": 2019,93 "venue": "European Journal of Operational Research",94 "url": "https://doi.org/10.1016/j.ejor.2018.09.030",95 "verified": true,96 "verifiedAt": "2026-10-30T17:18:09.229Z",97 "verificationMethod": "crossref",98 "accessLevel": "abstract",99 "claimedTitle": "Computational approaches for zero forcing and related problems",100 "titleSimilarity": 1101 },102 {103 "key": "brimkov2021improved",104 "kind": "doi",105 "identifier": "10.1287/ijoc.2020.1032",106 "title": "Improved Computational Approaches and Heuristics for Zero Forcing",107 "authors": [108 "Brimkov, Boris",109 "Mikesell, Derek",110 "Hicks, Illya V."111 ],112 "year": 2021,113 "venue": "INFORMS Journal on Computing",114 "url": "https://doi.org/10.1287/ijoc.2020.1032",115 "verified": true,116 "verifiedAt": "2026-10-30T17:18:09.297Z",117 "verificationMethod": "crossref",118 "accessLevel": "abstract",119 "claimedTitle": "Improved Computational Approaches and Heuristics for Zero Forcing",120 "titleSimilarity": 1121 },122 {123 "key": "alameda2018families",124 "kind": "doi",125 "identifier": "10.1515/spma-2018-0006",126 "title": "Families of graphs with maximum nullity equal to zero forcing number",127 "authors": [128 "Alameda, Joseph S.",129 "Curl, Emelie",130 "Grez, Armando",131 "Hogben, Leslie",132 "Kingston, O’Neill",133 "Schulte, Alex",134 "Young, Derek",135 "Young, Michael"136 ],137 "year": 2018,138 "venue": "Special Matrices",139 "url": "https://doi.org/10.1515/spma-2018-0006",140 "verified": true,141 "verifiedAt": "2026-10-30T17:18:09.354Z",142 "verificationMethod": "crossref",143 "accessLevel": "abstract",144 "claimedTitle": "Families of graphs with maximum nullity equal to zero forcing number",145 "titleSimilarity": 1146 },147 {148 "key": "watkins1969tait",149 "kind": "doi",150 "identifier": "10.1016/s0021-9800(69)80116-x",151 "title": "A theorem on tait colorings with an application to the generalized Petersen graphs",152 "authors": [153 "Watkins, Mark E."154 ],155 "year": 1969,156 "venue": "Journal of Combinatorial Theory",157 "url": "https://doi.org/10.1016/s0021-9800(69)80116-x",158 "verified": true,159 "verifiedAt": "2026-10-30T17:18:09.408Z",160 "verificationMethod": "crossref",161 "accessLevel": "metadata",162 "claimedTitle": "A theorem on tait colorings with an application to the generalized Petersen graphs",163 "titleSimilarity": 1164 },165 {166 "key": "frucht1971groups",167 "kind": "doi",168 "identifier": "10.1017/s0305004100049811",169 "title": "The groups of the generalized Petersen graphs",170 "authors": [171 "Frucht, Roberto",172 "Graver, Jack E.",173 "Watkins, Mark E."174 ],175 "year": 1971,176 "venue": "Mathematical Proceedings of the Cambridge Philosophical Society",177 "url": "https://doi.org/10.1017/s0305004100049811",178 "verified": true,179 "verifiedAt": "2026-10-30T17:18:09.464Z",180 "verificationMethod": "crossref",181 "accessLevel": "abstract",182 "claimedTitle": "The groups of the generalized Petersen graphs",183 "titleSimilarity": 1184 },185 {186 "key": "wetzler2014drattrim",187 "kind": "doi",188 "identifier": "10.1007/978-3-319-09284-3_31",189 "title": "DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs",190 "authors": [191 "Wetzler, Nathan",192 "Heule, Marijn J. 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