{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T20:55:39Z","timestamp":1757451339400},"reference-count":15,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":4850,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1993,7]]},"abstract":"Abstract<\/jats:title>In the application of graph theory to problems arising in network design, the requirements of the network can be expressed in terms of restrictions on the values of certain graph parameters such as connectivity, edge\u2010connectivity, diameter, and independence number. In this paper, we focus on networks whose requirements translate into adjacency restrictions on the graph representing the network. More specifically, a graph G<\/jats:italic> is said to have property P(m,n,k)<\/jats:italic> if for any set of m<\/jats:italic> + n<\/jats:italic> distinct vertices there are at least k<\/jats:italic> other vertices, each of which is adjacent to the first m<\/jats:italic> vertices but not adjacent to any of the latter n<\/jats:italic> vertices. The problem that arises is that of characterizing graphs having property P(m,n,k)<\/jats:italic>. In this paper, we present properties of graphs satisfying the adjacency property. In particular, for q<\/jats:italic> \uf8fd 1(mod 4), a prime power, the Paley graph G<\/jats:italic>q<\/jats:italic><\/jats:sub> of order q<\/jats:italic> is the graph whose vertices are elements of the finite field \ud835\udd3dq<\/jats:italic><\/jats:sub>; two vertices are adjacent if and only if their difference is a quadratic residue. For any m, n<\/jats:italic>, and k<\/jats:italic>, we show that all sufficiently large Paley graphs satisfy P(m,n,k)<\/jats:italic>. \u00a9 1993 by John Wiley & Sons, Inc.<\/jats:italic><\/jats:p>","DOI":"10.1002\/net.3230230404","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T14:21:41Z","timestamp":1178979701000},"page":"227-236","source":"Crossref","is-referenced-by-count":18,"title":["On the adjacency properties of paley graphs"],"prefix":"10.1002","volume":"23","author":[{"given":"W.","family":"Ananchuen","sequence":"first","affiliation":[]},{"given":"L.","family":"Caccetta","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"155","article-title":"Graphs with a prescribed adjacency property","volume":"6","author":"Ananchuen W.","year":"1992","journal-title":"Aust. J. Comb."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030305"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050414"},{"key":"e_1_2_1_5_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_6_2","volume-title":"Graph Theory with Applications","author":"Bondy J. A.","year":"1977"},{"key":"e_1_2_1_7_2","unstructured":"L.Caccetta Graph theory in network designs and analysis.Recent Stud. Graph Theory(1989)26\u201363."},{"key":"e_1_2_1_8_2","first-page":"287","article-title":"A property of random graphs","volume":"19","author":"Caccetta L.","year":"1985","journal-title":"ARS Comb."},{"key":"e_1_2_1_9_2","first-page":"21","article-title":"On minimal graphs with prescribed adjacency property","volume":"21","author":"Caccetta L.","year":"1986","journal-title":"ARS Comb."},{"key":"e_1_2_1_10_2","first-page":"93","article-title":"On strongly accessible graphs","volume":"17","author":"Caccetta L.","year":"1984","journal-title":"ARS Comb."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190050406"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90283-N"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1970.tb56466.x"},{"key":"e_1_2_1_14_2","volume-title":"Finite Fields","author":"Lidl R.","year":"1983"},{"key":"e_1_2_1_15_2","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0080437","volume-title":"Equations over Finite Fields, An Elementary Approach","author":"Schmidt W. M.","year":"1976"},{"key":"e_1_2_1_16_2","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0069907","volume-title":"Combinatorics Room Squares, Sum\u2010Free Sets, Hadamard Matrices","author":"Wallis W. D.","year":"1972"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230230404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230230404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T03:37:15Z","timestamp":1698205035000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230230404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,7]]}},"alternative-id":["10.1002\/net.3230230404"],"URL":"https:\/\/doi.org\/10.1002\/net.3230230404","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,7]]}}}