{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:16:34Z","timestamp":1753884994005,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"name":"maple league of universities"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> In this paper, we explore a variant of the game of Cops and Robber introduced by Bonato et al. where the robber is invisible unless outside the common neighborhood of the cops. The hyperopic cop number is analogous to the cop number and we investigate bounds on this quantity. We define a small common neighborhood set and relate the minimum cardinality of this graph parameter to the hyperopic cop number. We consider diameter [Formula: see text] graphs, particularly the join of two graphs, as well as Cartesian products. <\/jats:p>","DOI":"10.1142\/s1793830922501270","type":"journal-article","created":{"date-parts":[[2022,6,24]],"date-time":"2022-06-24T07:39:45Z","timestamp":1656056385000},"source":"Crossref","is-referenced-by-count":0,"title":["A note on hyperopic cops and robber"],"prefix":"10.1142","volume":"15","author":[{"given":"N. E.","family":"Clarke","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Acadia University, Wolfville, NS, Canada"}]},{"given":"S.","family":"Finbow","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, St. Francis Xavier University, Antigonish, NS, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1153-0926","authenticated-orcid":false,"given":"M. E.","family":"Messinger","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada"}]},{"given":"A.","family":"Porter","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada"}]}],"member":"219","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"S1793830922501270BIB001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0166-218X(84)90073-8","volume":"8","author":"Aigner M.","year":"1984","journal-title":"Discret. Appl. Math."},{"key":"S1793830922501270BIB002","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1006\/aama.1993.1019","volume":"14","author":"Berarducci A.","year":"1993","journal-title":"Adv. Appl. Math."},{"key":"S1793830922501270BIB003","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.tcs.2018.10.004","volume":"794","author":"Bonato A.","year":"2018","journal-title":"Theor. Comput. Sci."},{"key":"S1793830922501270BIB004","doi-asserted-by":"crossref","DOI":"10.1090\/stml\/061","volume-title":"The Game of Cops and Robbers on Graphs","author":"Bonato A.","year":"2011"},{"key":"S1793830922501270BIB005","first-page":"97","volume":"56","author":"Clarke N. E.","year":"2000","journal-title":"Ars Comb."},{"key":"S1793830922501270BIB006","first-page":"52","volume":"282","author":"Cox D.","year":"2020","journal-title":"Discret. Appl. Math."},{"key":"S1793830922501270BIB007","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.tcs.2015.03.022","volume":"607","author":"Dereniowski D.","year":"2015","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"S1793830922501270BIB008","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10878-014-9712-6","volume":"29","author":"Dereniowski D.","year":"2015","journal-title":"J. Comb. Optim."},{"key":"S1793830922501270BIB009","unstructured":"R. To\u0161i\u0107 ,  On Cops and Robber Game,  Studia Scientiarum Mathematicarum Hungarcia,  23rd edn.  (Yugoslavia,  1988),  pp. 225\u2013229."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501270","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,23]],"date-time":"2023-05-23T03:18:07Z","timestamp":1684811887000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501270"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,29]]},"references-count":9,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["10.1142\/S1793830922501270"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501270","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,7,29]]},"article-number":"2250127"}}