{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T01:28:28Z","timestamp":1755221308523,"version":"3.43.0"},"reference-count":14,"publisher":"National Library of Serbia","issue":"7","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/publicdomain\/zero\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Filomat"],"published-print":{"date-parts":[[2025]]},"abstract":"<jats:p>Two non isomorphic graphs G and H are said to be cospectral, if they share the same adjacency eigenvalues. In this paper, we use a recursive procedure for computing the characteristic polynomial of chain graphs in order to obtain infinitely many pairs of connected cospectral chain graphs. This result disproves a conjecture posed in [Czechoslovak Math. J. 70 (4) (2020), 1125-1138]. In addition we construct infinite families of bipartite graphs sharing the same spectrum.<\/jats:p>","DOI":"10.2298\/fil2507171a","type":"journal-article","created":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T13:34:57Z","timestamp":1754660097000},"page":"2171-2177","source":"Crossref","is-referenced-by-count":0,"title":["Chain graphs are not spectrally determined"],"prefix":"10.2298","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3348-1141","authenticated-orcid":false,"given":"Milica","family":"Andjelic","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Kuwait University, Al-Shadadiyah, Kuwait"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5423-7191","authenticated-orcid":false,"suffix":"C.","given":"Fernando","family":"Tura","sequence":"additional","affiliation":[{"name":"Departamentode Matem\u00e1tica, Universidade Federalde Santa Maria, Santa Maria, Rio Grande do Sul, Brazil"}]}],"member":"1078","reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"A. Alazemi, M. An\u0111eli\u0107, S.K. Simi\u0107, Eigenvalue location for chain graphs, Linear Algebra Appl. 505 (2016), 194-210.","DOI":"10.1016\/j.laa.2016.04.030"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"M. An\u0111eli\u0107, S.K. Simi\u0107, D. \u017divkovi\u0107, E. Doli\u0107anin, Fast algorithms for computing the characteristic polynomial of threshold and chain graphs, Appl. Math. Comput. 332 (2018), 329\u2013337.","DOI":"10.1016\/j.amc.2018.03.024"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"M. An\u0111eli\u0107, Z. Du, C.M. da Fonseca, S.K. Simi\u0107, Tridiagonal matrices and spectral properties of some graph classes, Czechoslovak Math. J. 70 4 (2020), 1125\u20131138.","DOI":"10.21136\/CMJ.2020.0182-19"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"A. Bhattacharya, S. Friesland, U.N. Peled, On the first eigenvalue of bipartite graphs, Electron. J.Combin., 15 (2008), 144","DOI":"10.37236\/868"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, Berlin, 2012.","DOI":"10.1007\/978-1-4614-1939-6"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"J. Carvalho, B. S. Souza, V. Trevisan, F. C. Tura, Exponentially many graphs have a Q-cospectral mate, Discrete Math. 340 (2017), 2079\u20132085.","DOI":"10.1016\/j.disc.2017.04.009"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"C. D. Godsil, B. D. McKay, Constructing cospectral graphs, Aequationes Math. 25 (1982), 257\u2013268.","DOI":"10.1007\/BF02189621"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"C. Godsil, B. McKay, Some computational results on the spectra of graphs, in: Combinatorial Mathematics, IV (Proc. Fourth Australian Conf., Univ. Adelaide, Adelaide, 1975), in: Lecture Notes in Math., 560, Springer, Berlin, 1976, pp. 73\u201392.","DOI":"10.1007\/BFb0097370"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"C. Godsil, G. Royle, Algebraic Graph Theory, Springer-Verlag, New York, 2001.","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"S. C. Gong, L. P. Zhang, S.W. Sun, On Bipartite Graphs Having Minimum Fourth Adjacency Coefficient, Graphs Combin. 38, 60 (2022)","DOI":"10.1007\/s00373-022-02461-7"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"E. R. van Dam, W. H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241\u2013272.","DOI":"10.1016\/S0024-3795(03)00483-X"},{"key":"ref12","unstructured":"P. Heggernes, D. Kratsch, Linear-time certifying recognition algorithms and forbidden induced subgraphs, Nordic. J.Comput. 14 (2007), 87\u2013108."},{"key":"ref13","unstructured":"B. D. McKay, On the spectral characterisation of trees, Ars Combin. (ISSN: 0381-7032) 3 (1977), 219\u2013232."},{"key":"ref14","unstructured":"A. J. Schwenk, Almost all trees are cospectral, in: New Directions in the Theory of Graphs (Proc. Third Ann Arbor Conf., Univ. Michigan, Ann Arbor, Mich., 1971), Academic Press, New York, 1973, pp. 275\u2013307."}],"container-title":["Filomat"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T13:34:59Z","timestamp":1754660099000},"score":1,"resource":{"primary":{"URL":"https:\/\/doiserbia.nb.rs\/Article.aspx?ID=0354-51802507171A"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":14,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.2298\/fil2507171a","relation":{},"ISSN":["0354-5180","2406-0933"],"issn-type":[{"value":"0354-5180","type":"print"},{"value":"2406-0933","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]}}}