The localization number of designs
We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph G, written ζ ( G ), is the minimum number of cops needed to ensure th...
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| Veröffentlicht in: | Journal of combinatorial designs 2021-03, Vol.29 (3), p.175-192 |
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| container_title | Journal of combinatorial designs |
| container_volume | 29 |
| creator | Bonato, Anthony Huggan, Melissa A. Marbach, Trent G. |
| description | We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph
G, written
ζ
(
G
), is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs. |
| doi_str_mv | 10.1002/jcd.21762 |
| format | Article |
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G, written
ζ
(
G
), is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.</description><identifier>ISSN: 1063-8539</identifier><identifier>EISSN: 1520-6610</identifier><identifier>DOI: 10.1002/jcd.21762</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc</publisher><subject>balanced incomplete block designs ; Graphs ; incidence graphs ; Localization ; localization number ; projective planes ; Steiner systems</subject><ispartof>Journal of combinatorial designs, 2021-03, Vol.29 (3), p.175-192</ispartof><rights>2020 Wiley Periodicals LLC</rights><rights>2021 Wiley Periodicals LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2972-4d9343c041afcc60481783f60d4f48de3d1861bc836834b4d61da68e07de5e493</citedby><cites>FETCH-LOGICAL-c2972-4d9343c041afcc60481783f60d4f48de3d1861bc836834b4d61da68e07de5e493</cites><orcidid>0000-0003-3969-5412</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fjcd.21762$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fjcd.21762$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Bonato, Anthony</creatorcontrib><creatorcontrib>Huggan, Melissa A.</creatorcontrib><creatorcontrib>Marbach, Trent G.</creatorcontrib><title>The localization number of designs</title><title>Journal of combinatorial designs</title><description>We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph
G, written
ζ
(
G
), is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.</description><subject>balanced incomplete block designs</subject><subject>Graphs</subject><subject>incidence graphs</subject><subject>Localization</subject><subject>localization number</subject><subject>projective planes</subject><subject>Steiner systems</subject><issn>1063-8539</issn><issn>1520-6610</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kDtPwzAUhS0EEqUw8A8imBjSXj_i2CMK5aVKLGW2HD8gURoXuxEqv55AWJnuGb5zrvQhdIlhgQHIsjV2QXDJyRGa4YJAzjmG4zEDp7koqDxFZym1ACAl5TN0tXl3WReM7povvW9Cn_XDtnYxCz6zLjVvfTpHJ153yV383Tl6vV9tqsd8_fLwVN2uc0NkSXJmJWXUAMPaG8OBCVwK6jlY5pmwjlosOK6NoFxQVjPLsdVcOCitKxyTdI6up91dDB-DS3vVhiH240tFWFkQIYDwkbqZKBNDStF5tYvNVseDwqB-FKhRgfpVMLLLif1sOnf4H1TP1d3U-AY7q1qO</recordid><startdate>202103</startdate><enddate>202103</enddate><creator>Bonato, Anthony</creator><creator>Huggan, Melissa A.</creator><creator>Marbach, Trent G.</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-3969-5412</orcidid></search><sort><creationdate>202103</creationdate><title>The localization number of designs</title><author>Bonato, Anthony ; Huggan, Melissa A. ; Marbach, Trent G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2972-4d9343c041afcc60481783f60d4f48de3d1861bc836834b4d61da68e07de5e493</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>balanced incomplete block designs</topic><topic>Graphs</topic><topic>incidence graphs</topic><topic>Localization</topic><topic>localization number</topic><topic>projective planes</topic><topic>Steiner systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bonato, Anthony</creatorcontrib><creatorcontrib>Huggan, Melissa A.</creatorcontrib><creatorcontrib>Marbach, Trent G.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of combinatorial designs</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bonato, Anthony</au><au>Huggan, Melissa A.</au><au>Marbach, Trent G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The localization number of designs</atitle><jtitle>Journal of combinatorial designs</jtitle><date>2021-03</date><risdate>2021</risdate><volume>29</volume><issue>3</issue><spage>175</spage><epage>192</epage><pages>175-192</pages><issn>1063-8539</issn><eissn>1520-6610</eissn><abstract>We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph
G, written
ζ
(
G
), is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/jcd.21762</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0003-3969-5412</orcidid></addata></record> |
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| ispartof | Journal of combinatorial designs, 2021-03, Vol.29 (3), p.175-192 |
| issn | 1063-8539 1520-6610 |
| language | eng |
| recordid | cdi_proquest_journals_2475288026 |
| source | Wiley Online Library All Journals |
| subjects | balanced incomplete block designs Graphs incidence graphs Localization localization number projective planes Steiner systems |
| title | The localization number of designs |
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