{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T19:26:21Z","timestamp":1746905181610,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,1]],"date-time":"2021-05-01T00:00:00Z","timestamp":1619827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/MAT\/00297\/2019"],"award-info":[{"award-number":["UID\/MAT\/00297\/2019"]}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PTDC\/MAT-PUR\/31174\/2017"],"award-info":[{"award-number":["PTDC\/MAT-PUR\/31174\/2017"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["K115518"],"award-info":[{"award-number":["K115518"]}],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005881","name":"Emberi Eroforr\u00e1sok Miniszt\u00e9riuma","doi-asserted-by":"publisher","award":["TUDFO\/47138-1\/2019-ITM"],"award-info":[{"award-number":["TUDFO\/47138-1\/2019-ITM"]}],"id":[{"id":"10.13039\/501100005881","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University of Szeged Open Access Fund","award":["4468"],"award-info":[{"award-number":["4468"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Algebr Comb"],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.<\/jats:p>","DOI":"10.1007\/s10801-020-01010-w","type":"journal-article","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T19:52:31Z","timestamp":1620071551000},"page":"613-638","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Associative spectra of graph algebras I"],"prefix":"10.1007","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9255-5876","authenticated-orcid":false,"given":"Erkko","family":"Lehtonen","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0365-6497","authenticated-orcid":false,"given":"Tam\u00e1s","family":"Waldhauser","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,3]]},"reference":[{"key":"1010_CR1","doi-asserted-by":"crossref","unstructured":"Berman, J., Burris, S.: A computer study of 3\u2013element groupoids. In: Ursini, A., Aglian\u00f2 P. (eds.), Logic and Algebra (Pontignano, 1994). Lecture Notes in Pure and Appl. Math., 180, pp. 379\u2013429. Dekker, New York (1996)","DOI":"10.1201\/9780203748671-18"},{"key":"1010_CR2","doi-asserted-by":"publisher","first-page":"79","DOI":"10.21136\/MB.2012.142789","volume":"137","author":"M Braitt","year":"2012","unstructured":"Braitt, M., Hobby, D., Silberger, D.: Completely dissociative groupoids. Math. Bohem. 137, 79\u201397 (2012)","journal-title":"Math. Bohem."},{"key":"1010_CR3","doi-asserted-by":"publisher","first-page":"27","DOI":"10.21136\/MB.2017.0006-15","volume":"142","author":"M Braitt","year":"2017","unstructured":"Braitt, M., Hobby, D., Silberger, D.: Antiassociative groupoids. Math. Bohem. 142, 27\u201346 (2017)","journal-title":"Math. Bohem."},{"key":"1010_CR4","first-page":"11","volume":"14","author":"MS Braitt","year":"2006","unstructured":"Braitt, M.S., Silberger, D.: Subassociative groupoids. Quasigroups Related Systems 14, 11\u201326 (2006)","journal-title":"Quasigroups Related Systems"},{"key":"1010_CR5","unstructured":"Climescu, A.C.: \u00c9tudes sur la th\u00e9orie des syst\u00e8mes multiplicatifs uniformes I. L\u2019indice de non-associativit\u00e9. Bull. \u00c9cole Polytech. Jassy 2, 347\u2013371 (1947) (French)"},{"key":"1010_CR6","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2001","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, McGraw-Hill (2001)","edition":"2"},{"key":"1010_CR7","first-page":"175","volume":"5","author":"B Cs\u00e1k\u00e1ny","year":"2000","unstructured":"Cs\u00e1k\u00e1ny, B., Waldhauser, T.: Associative spectra of binary operations. Mult.-Valued Log. 5, 175\u2013200 (2000)","journal-title":"Mult.-Valued Log."},{"key":"1010_CR8","doi-asserted-by":"crossref","unstructured":"de Bruijn, N.G., Knuth, D.E., Rice, S.O.: The average height of planted plane trees. Graph theory and computing, pp. 15\u201322. Academic Press, New York (1972)","DOI":"10.1016\/B978-1-4832-3187-7.50007-6"},{"key":"1010_CR9","volume-title":"Universal Algebra and Applications in Theoretical Computer Science","author":"K Denecke","year":"2002","unstructured":"Denecke, K., Wismath, S.L.: Universal Algebra and Applications in Theoretical Computer Science. Chapman & Hall\/CRC, Boca Raton (2002)"},{"key":"1010_CR10","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/j.ejc.2016.11.004","volume":"61","author":"N Hein","year":"2017","unstructured":"Hein, N., Huang, J.: Modular Catalan numbers. European J. Combin. 61, 197\u2013218 (2017)","journal-title":"European J. Combin."},{"key":"1010_CR11","first-page":"69","volume":"33","author":"T Kepka","year":"1992","unstructured":"Kepka, T., Trch, M.: Groupoids and the associative law I. (Associative triples). Acta Univ. Carol. Math. Phys. 33, 69\u201386 (1992)","journal-title":"Acta Univ. Carol. Math. Phys."},{"key":"1010_CR12","first-page":"67","volume":"34","author":"T Kepka","year":"1993","unstructured":"Kepka, T., Trch, M.: Groupoids and the associative law II. (Groupoids with small semigroup distance). Acta Univ. Carol. Math. Phys. 34, 67\u201383 (1993)","journal-title":"Acta Univ. Carol. Math. Phys."},{"key":"1010_CR13","doi-asserted-by":"crossref","unstructured":"Kiss, E.W.: A note on varieties of graph algebras. Universal algebra and lattice theory. Lecture Notes in Math., 1149, pp. 163\u2013166. Springer, Berlin (1985)","DOI":"10.1007\/BFb0098463"},{"key":"1010_CR14","first-page":"433","volume":"75","author":"S Liebscher","year":"2009","unstructured":"Liebscher, S., Waldhauser, T.: On associative spectra of operations. Acta Sci. Math. (Szeged) 75, 433\u2013456 (2009)","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"1010_CR15","doi-asserted-by":"publisher","first-page":"169","DOI":"10.7151\/dmgaa.1014","volume":"20","author":"T Poomsa-ard","year":"2000","unstructured":"Poomsa-ard, T.: Hyperidentities in associative graph algebras. Discuss. Math. Gen. Algebra Appl. 20, 169\u2013182 (2000)","journal-title":"Discuss. Math. Gen. Algebra Appl."},{"key":"1010_CR16","first-page":"581","volume":"28","author":"R P\u00f6schel","year":"1987","unstructured":"P\u00f6schel, R., Wessel, W.: Classes of graphs definable by graph algebra identities or quasi-identities. Comment. Math. Univ. Carolin. 28, 581\u2013592 (1987)","journal-title":"Comment. Math. Univ. Carolin."},{"key":"1010_CR17","unstructured":"Shallon, C.R.: Non-finitely based binary algebras derived from lattices. Ph.D. thesis. University of California, Los Angeles (1979)"},{"key":"1010_CR18","unstructured":"Stanley, R.P.: Enumerative combinatorics Vol. 2. Cambridge Studies in Advanced Mathematics, 62. Cambridge University Press, Cambridge (1999)"},{"key":"1010_CR19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139871495","volume-title":"Catalan Numbers","author":"RP Stanley","year":"2015","unstructured":"Stanley, R.P.: Catalan Numbers. Cambridge University Press, New York (2015)"}],"container-title":["Journal of Algebraic Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10801-020-01010-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10801-020-01010-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10801-020-01010-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,12]],"date-time":"2021-05-12T13:51:47Z","timestamp":1620827507000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10801-020-01010-w"}},"subtitle":["Foundations, undirected graphs, antiassociative graphs"],"short-title":[],"issued":{"date-parts":[[2021,5]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["1010"],"URL":"https:\/\/doi.org\/10.1007\/s10801-020-01010-w","relation":{},"ISSN":["0925-9899","1572-9192"],"issn-type":[{"type":"print","value":"0925-9899"},{"type":"electronic","value":"1572-9192"}],"subject":[],"published":{"date-parts":[[2021,5]]},"assertion":[{"value":"29 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}