{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T05:30:36Z","timestamp":1776231036256,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:p> A [Formula: see text]-design over regular graph [Formula: see text] of degree [Formula: see text] is an ordered pair [Formula: see text], where [Formula: see text] and [Formula: see text] is the set of geodetic sets in [Formula: see text] called blocks such that two vertices [Formula: see text] and [Formula: see text] which are [Formula: see text] associates occur together in [Formula: see text] blocks, the numbers [Formula: see text] being independent of the choice of the pair [Formula: see text] and [Formula: see text]. In this paper, we obtain Partially Balanced Incomplete Block (PBIB)-designs arising from geodetic sets in some classes of graphs. Also, we give a complete list of PBIB-designs with respect to the geodetic sets for cubic graphs of order at most [Formula: see text]. The discussion of non-existence of some designs corresponding to geodetic sets from certain graphs concludes the paper. <\/jats:p>","DOI":"10.1142\/s1793830922500598","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T01:55:46Z","timestamp":1645581346000},"source":"Crossref","is-referenced-by-count":3,"title":["Partially balanced incomplete block (PBIB)-designs associated with geodetic sets in graphs"],"prefix":"10.1142","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1548-1794","authenticated-orcid":false,"given":"Medha Itagi","family":"Huilgol","sequence":"first","affiliation":[{"name":"Department of Mathematics, Bengaluru City University, Central College Campus, Bengaluru 560001, India"}]},{"given":"M. D.","family":"Vidya","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bangalore University, Bengaluru 560056, India"}]}],"member":"219","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"S1793830922500598BIB001","volume-title":"Theory of Graphs and its Applications","author":"Berge C.","year":"1962"},{"key":"S1793830922500598BIB002","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1990"},{"key":"S1793830922500598BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/net.10007"},{"key":"S1793830922500598BIB005","first-page":"37","volume":"156","author":"Chartrand G.","year":"2002","journal-title":"Congr. Numer."},{"key":"S1793830922500598BIB006","volume-title":"Handbook of Combinatorial Designs","author":"Colbourn C. J.","year":"2007","edition":"2"},{"key":"S1793830922500598BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0895-7177(93)90259-2"},{"key":"S1793830922500598BIB010","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0378-3758(00)00289-5","volume":"95","author":"Ionin Y. J.","year":"2001","journal-title":"J. Stat. Plann. Inference"},{"key":"S1793830922500598BIB011","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/S0021-9800(66)80010-8","volume":"1","author":"Paola J. W.","year":"1966","journal-title":"J. Comb. Theory"},{"key":"S1793830922500598BIB012","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0012-365X(83)90271-6","volume":"46","author":"Parthasarathy K. R.","year":"1983","journal-title":"Discrete Math."},{"key":"S1793830922500598BIB013","volume-title":"Construction and Combinatorial Problems in Design of Experiments","author":"Raghavarao D.","year":"1971"},{"key":"S1793830922500598BIB014","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10623-009-9351-6","volume":"57","author":"Walikar H. B.","year":"2010","journal-title":"Des. Codes Cryptogr."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500598","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T05:24:18Z","timestamp":1675401858000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500598"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,22]]},"references-count":11,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["10.1142\/S1793830922500598"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500598","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,22]]},"article-number":"2250059"}}