{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T06:35:41Z","timestamp":1723271741624},"reference-count":14,"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":"<jats:title>Abstract<\/jats:title><jats:p>For a given graph <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic>, a routing <jats:italic>R<\/jats:italic> is a set of <jats:italic>n<\/jats:italic>(<jats:italic>n<\/jats:italic> \u2212 1) elementary paths specified for every ordered pair of vertices in <jats:italic>G<\/jats:italic>. The edge forwarding index of a network <jats:italic>(G,R)<\/jats:italic>, denoted \u03c0<jats:italic>(G,R)<\/jats:italic> is the maximum number of paths of <jats:italic>R<\/jats:italic> going through any edge <jats:italic>e<\/jats:italic> of <jats:italic>G<\/jats:italic>. The edge forwarding index of <jats:italic>G<\/jats:italic>, denoted \u03c0<jats:italic>(G)<\/jats:italic>, is the minimum of \u03c0<jats:italic>(G,R)<\/jats:italic> taken over all the possible routings <jats:italic>R<\/jats:italic> of <jats:italic>G<\/jats:italic>. Given <jats:italic>n<\/jats:italic> \u2264 15 and \u0394 \u2264 <jats:italic>n<\/jats:italic> \u2212 1 we determine \u03c0<jats:sub>\u0394,<jats:italic>n<\/jats:italic><\/jats:sub>, the minimum of \u03c0<jats:italic>(G)<\/jats:italic> taken over all graphs <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic> with maximum degree at most \u0394. This is known as the edge forwarding index problem. \u00a9 <jats:italic>1993 by John Wiley &amp; Sons, Inc.<\/jats:italic><\/jats:p>","DOI":"10.1002\/net.3230230406","type":"journal-article","created":{"date-parts":[[2007,5,12]],"date-time":"2007-05-12T14:21:31Z","timestamp":1178979691000},"page":"249-255","source":"Crossref","is-referenced-by-count":16,"title":["On the edge forwarding index problem for small graphs"],"prefix":"10.1002","volume":"23","author":[{"given":"Abdelmadjid","family":"Bouabdallah","sequence":"first","affiliation":[]},{"given":"Dominique","family":"Sotteau","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1939.tb02219.x"},{"key":"e_1_2_1_4_2","unstructured":"A.Bouabdallah Ar\u011bte\u2010indice de transmission dans les r\u00e9seux. Repport DEA LRI (Orsay) (Sept.1988)."},{"key":"e_1_2_1_5_2","first-page":"87","article-title":"Generalized Moore graphs on twelve and thirteen vertices","volume":"23","author":"Buskens R. W.","year":"1987","journal-title":"Ars Comb."},{"key":"e_1_2_1_6_2","first-page":"51","article-title":"A census of tetravalent GM graphs on fourteen to twenty vertices","volume":"2","author":"Buskens R. W.","year":"1987","journal-title":"J. Comb. Math. Comb. Comput."},{"key":"e_1_2_1_7_2","unstructured":"S.Bussemaker L.Cobeljic M.Cvetkovic andJ. J.Seidel Computer investigation of cubic graphs. Research Report No. 76\u2014WSK\u201401 University of Heindoven (1976)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1987.1057290"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)90129-X"},{"key":"e_1_2_1_10_2","unstructured":"M.Hall Jr. Difference sets.Combinatorics Part 3: Combinatorial Group Theory.Proc. Advanced Study Inst. Breukelen 1974. Math. Centre Tracts 57 Math. Centrum Amsterdam (1974)1\u201326."},{"key":"e_1_2_1_11_2","unstructured":"M.\u2010C.Heydemann J.\u2010C.Meyer andD.Sotteau On the forwarding index problem for small graphs.Ars Combinatoria Proceedings of the British Combinatorial Conference London(1988)253\u2013266."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(89)90022-X"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"M.\u2010C.Heydemann J.\u2010C.Meyer andD.Sotteau Forwarding indices of consistent routings and their complexity. Research Report No. 496 LRI (Orsay) (1989).Networks to appear.","DOI":"10.1016\/0166-218X(89)90022-X"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)90140-6"},{"key":"e_1_2_1_15_2","unstructured":"D.Sotteau Th\u00e8se d'\u00e9tat. University of Paris\u2010Sud (Orsay) (1980)."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230230406","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230230406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T03:37:24Z","timestamp":1698205044000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230230406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,7]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1993,7]]}},"alternative-id":["10.1002\/net.3230230406"],"URL":"https:\/\/doi.org\/10.1002\/net.3230230406","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]]}}}