{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:20:23Z","timestamp":1772119223168,"version":"3.50.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T00:00:00Z","timestamp":1708905600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T00:00:00Z","timestamp":1708905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Acta Informatica"],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s00236-024-00454-y","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T11:02:11Z","timestamp":1708945331000},"page":"115-129","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New families of Laplacian borderenergetic graphs"],"prefix":"10.1007","volume":"61","author":[{"given":"Cahit","family":"Dede","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,2,26]]},"reference":[{"key":"454_CR1","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1007\/978-3-642-59448-9_13","volume-title":"Algebraic combinatorics and applications","author":"I Gutman","year":"2001","unstructured":"Gutman, I.: The energy of a graph: old and new results. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds.) Algebraic combinatorics and applications, pp. 196\u2013211. Springer, Berlin, Heidelberg (2001)"},{"key":"454_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4220-2_2","author":"X Li","year":"2012","unstructured":"Li, X., Shi, Y., Gutman, I.: The chemical connection. Graph Energy (2012). https:\/\/doi.org\/10.1007\/978-1-4614-4220-2_2","journal-title":"Graph Energy"},{"issue":"2","key":"454_CR3","doi-asserted-by":"publisher","first-page":"1472","DOI":"10.1016\/j.jmaa.2006.03.072","volume":"326","author":"V Nikiforov","year":"2007","unstructured":"Nikiforov, V.: The energy of graphs and matrices. J. Math. Anal. Appl. 326(2), 1472\u20131475 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"454_CR4","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1016\/j.disc.2014.02.017","volume":"325","author":"KC Das","year":"2014","unstructured":"Das, K.C., Mojallal, S.A.: On Laplacian energy of graphs. Discret. Math. 325, 52\u201364 (2014)","journal-title":"Discret. Math."},{"key":"454_CR5","first-page":"83","volume":"268","author":"KC Das","year":"2015","unstructured":"Das, K.C., Mojallal, S.A., Gutman, I.: On Laplacian energy in terms of graph invariants. Appl. Math. Comput. 268, 83\u201392 (2015)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"454_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.2478\/ausi-2014-0020","volume":"6","author":"HA Ganie","year":"2014","unstructured":"Ganie, H.A., Pirzada, S., Iv\u00e1nyi, A.: Energy, Laplacian energy of double graphs and new families of equienergetic graphs. Acta Universitatis Sapientiae, Informatica 6(1), 89\u2013116 (2014)","journal-title":"Acta Universitatis Sapientiae, Informatica"},{"key":"454_CR7","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1016\/j.laa.2015.08.032","volume":"486","author":"S Pirzada","year":"2015","unstructured":"Pirzada, S., Ganie, H.A.: On the Laplacian eigenvalues of a graph and Laplacian energy. Linear Algebra Appl. 486, 454\u2013468 (2015)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"454_CR8","doi-asserted-by":"publisher","first-page":"94","DOI":"10.5614\/ejgta.2015.3.1.10","volume":"3","author":"HA Ganie","year":"2015","unstructured":"Ganie, H.A., Pirzada, S., Baskoro, E.T.: On energy, Laplacian energy and $$ p $$-fold graphs. Electron. J. Graph Theory Appl. 3(1), 94\u2013107 (2015)","journal-title":"Electron. J. Graph Theory Appl."},{"issue":"2","key":"454_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.5937\/KgJMath1502193R","volume":"39","author":"HS Ramane","year":"2015","unstructured":"Ramane, H.S., Gudodagi, G.A., Gutman, I.: Laplacian energy of union and cartesian product and Laplacian equienergetic graphs. Kragujevac J. Math. 39(2), 193\u2013205 (2015)","journal-title":"Kragujevac J. Math."},{"key":"454_CR10","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.dam.2016.09.030","volume":"228","author":"HA Ganie","year":"2017","unstructured":"Ganie, H.A., Pirzada, S.: On the bounds for signless Laplacian energy of a graph. Discret. Appl. Math. 228, 3\u201313 (2017)","journal-title":"Discret. Appl. Math."},{"key":"454_CR11","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1016\/j.laa.2018.01.021","volume":"544","author":"HA Ganie","year":"2018","unstructured":"Ganie, H.A., Chat, B.A., Pirzada, S.: Signless Laplacian energy of a graph and energy of a line graph. Linear Algebra Appl. 544, 306\u2013324 (2018)","journal-title":"Linear Algebra Appl."},{"key":"454_CR12","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.dam.2018.01.004","volume":"243","author":"KC Das","year":"2018","unstructured":"Das, K.C., Aouchiche, M., Hansen, P.: On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs. Discret. Appl. Math. 243, 172\u2013185 (2018)","journal-title":"Discret. Appl. Math."},{"key":"454_CR13","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/j.dam.2020.03.057","volume":"284","author":"KC Das","year":"2020","unstructured":"Das, K.C., Alazemi, A., Andelic, M.: On energy and Laplacian energy of chain graphs. Discret. Appl. Math. 284, 391\u2013400 (2020)","journal-title":"Discret. Appl. Math."},{"key":"454_CR14","volume":"366","author":"X Yang","year":"2020","unstructured":"Yang, X., Wang, L.: Extremal Laplacian energy of directed trees, unicyclic digraphs and bicyclic digraphs. Appl. Math. Comput. 366, 124737 (2020)","journal-title":"Appl. Math. Comput."},{"issue":"5","key":"454_CR15","doi-asserted-by":"publisher","first-page":"4847","DOI":"10.3934\/math.2021284","volume":"6","author":"Y Mei","year":"2021","unstructured":"Mei, Y., Guo, C., Liu, M.: The bounds of the energy and Laplacian energy of chain graphs. AIMS Math. 6(5), 4847\u20134859 (2021)","journal-title":"AIMS Math."},{"issue":"1","key":"454_CR16","doi-asserted-by":"publisher","first-page":"247","DOI":"10.46793\/match.90-1.247V","volume":"90","author":"DV Anchan","year":"2023","unstructured":"Anchan, D.V., D\u2019Souza, S., Gowtham, H., Bhat, P.G.: Laplacian energy of a graph with self-loops. Match 90(1), 247\u2013258 (2023)","journal-title":"Match"},{"key":"454_CR17","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/j.ins.2011.12.027","volume":"194","author":"X Qi","year":"2012","unstructured":"Qi, X., Fuller, E., Wu, Q., Wu, Y., Zhang, C.-Q.: Laplacian centrality: a new centrality measure for weighted networks. Inform. Sci. 194, 240\u2013253 (2012). https:\/\/doi.org\/10.1016\/j.ins.2011.12.027","journal-title":"Inform. Sci."},{"key":"454_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2017.07.007","volume":"716\u2013717","author":"N Masuda","year":"2017","unstructured":"Masuda, N., Porter, M.A., Lambiotte, R.: Random walks and diffusion on networks. Phys. Rep. 716\u2013717, 1\u201358 (2017). https:\/\/doi.org\/10.1016\/j.physrep.2017.07.007","journal-title":"Phys. Rep."},{"issue":"6","key":"454_CR19","doi-asserted-by":"publisher","first-page":"931","DOI":"10.1631\/FITEE.1900133","volume":"21","author":"M-D Hong","year":"2020","unstructured":"Hong, M.-D., Sun, W.-G., Liu, S.-Y., Xuan, T.-F.: Coherence analysis and Laplacian energy of recursive trees with controlled initial states. Front. Inform. Technol. Electron. Eng. 21(6), 931\u2013938 (2020)","journal-title":"Front. Inform. Technol. Electron. Eng."},{"issue":"6","key":"454_CR20","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1016\/j.automatica.2010.03.006","volume":"46","author":"W Yu","year":"2010","unstructured":"Yu, W., Chen, G., Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089\u20131095 (2010). https:\/\/doi.org\/10.1016\/j.automatica.2010.03.006","journal-title":"Automatica"},{"issue":"1","key":"454_CR21","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1016\/j.dam.2008.06.001","volume":"157","author":"H Fernau","year":"2009","unstructured":"Fernau, H., Rodr\u00edguez, J.A., Sigarreta, J.M.: Offensive r-alliances in graphs. Discret. Appl. Math. 157(1), 177\u2013182 (2009)","journal-title":"Discret. Appl. Math."},{"issue":"2","key":"454_CR22","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.akcej.2017.05.002","volume":"15","author":"K Ouazine","year":"2018","unstructured":"Ouazine, K., Slimani, H., Tari, A.: Alliances in graphs: parameters, properties and applications-a survey. AKCE Int. J. Graphs Comb. 15(2), 115\u2013154 (2018)","journal-title":"AKCE Int. J. Graphs Comb."},{"issue":"3","key":"454_CR23","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.physrep.2008.09.002","volume":"469","author":"A Arenas","year":"2008","unstructured":"Arenas, A., D\u00edaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Phys. Rep. 469(3), 93\u2013153 (2008). https:\/\/doi.org\/10.1016\/j.physrep.2008.09.002","journal-title":"Phys. Rep."},{"issue":"1","key":"454_CR24","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.physd.2006.09.018","volume":"224","author":"FM Atay","year":"2006","unstructured":"Atay, F.M., Biyikoglu, T., Jost, J.: Network synchronization: spectral versus statistical properties. Phys. D Nonlinear Phenom. 224(1), 35\u201341 (2006). https:\/\/doi.org\/10.1016\/j.physd.2006.09.018","journal-title":"Phys. D Nonlinear Phenom."},{"key":"454_CR25","doi-asserted-by":"publisher","unstructured":"Chen, J., Lu, J.-A., Zhan, C., Chen, G.: In: Thai, M.T., Pardalos, P.M. (eds.) Laplacian spectra and synchronization processes on complex networks, pp. 81\u2013113. Springer, Boston, MA (2012). https:\/\/doi.org\/10.1007\/978-1-4614-0754-6_4","DOI":"10.1007\/978-1-4614-0754-6_4"},{"key":"454_CR26","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.automatica.2016.06.012","volume":"73","author":"SE Tuna","year":"2016","unstructured":"Tuna, S.E.: Synchronization under matrix-weighted Laplacian. Automatica 73, 76\u201381 (2016). https:\/\/doi.org\/10.1016\/j.automatica.2016.06.012","journal-title":"Automatica"},{"key":"454_CR27","doi-asserted-by":"publisher","DOI":"10.1002\/9781119608165.ch1","volume-title":"Fractional dynamics on networks and lattices","author":"T Michelitsch","year":"2019","unstructured":"Michelitsch, T., Riascos, A.P., Collet, B., Nowakowski, A., Nicolleau, F.: Fractional dynamics on networks and lattices. Wiley, London (2019). https:\/\/doi.org\/10.1002\/9781119608165.ch1"},{"key":"454_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.comnet.2020.107697","volume":"184","author":"M Pushpalatha","year":"2021","unstructured":"Pushpalatha, M., Anusha, T., Rama Rao, T., Venkataraman, R.: L-rpl: Rpl powered by Laplacian energy for stable path selection during link failures in an Internet of Things network. Comput. Netw. 184, 107697 (2021). https:\/\/doi.org\/10.1016\/j.comnet.2020.107697","journal-title":"Comput. Netw."},{"key":"454_CR29","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.ast.2015.11.004","volume":"49","author":"C Yang","year":"2016","unstructured":"Yang, C., Mao, J., Wei, P.: Air traffic network optimization via Laplacian energy maximization. Aerosp. Sci. Technol. 49, 26\u201333 (2016). https:\/\/doi.org\/10.1016\/j.ast.2015.11.004","journal-title":"Aerosp. Sci. Technol."},{"issue":"9","key":"454_CR30","doi-asserted-by":"publisher","first-page":"949","DOI":"10.1080\/1351847X.2022.2091946","volume":"29","author":"C Huang","year":"2023","unstructured":"Huang, C., Deng, Y., Yang, X., Yang, X., Cao, J.: Can financial crisis be detected? Laplacian energy measure. Eur. J. Finance 29(9), 949\u2013976 (2023)","journal-title":"Eur. J. Finance"},{"issue":"2","key":"454_CR31","first-page":"321","volume":"74","author":"S Gong","year":"2015","unstructured":"Gong, S., Li, X., Xu, G., Gutman, I., Furtula, B.: Borderenergetic graphs. MATCH Commun. Math. Comput. Chem 74(2), 321\u2013332 (2015)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"key":"454_CR32","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.laa.2016.02.029","volume":"497","author":"B Deng","year":"2016","unstructured":"Deng, B., Li, X., Gutman, I.: More on borderenergetic graphs. Linear Algebra Appl. 497, 199\u2013208 (2016)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"454_CR33","first-page":"293","volume":"84","author":"M Ghorbani","year":"2020","unstructured":"Ghorbani, M., Deng, B., Hakimi-Nezhaad, M., Li, X.: A survey on borderenergetic graphs. MATCH Commun. Math. Comput. Chem 84(2), 293\u2013322 (2020)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"key":"454_CR34","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1016\/j.laa.2014.09.043","volume":"465","author":"DP Jacobs","year":"2015","unstructured":"Jacobs, D.P., Trevisan, V., Tura, F.: Eigenvalues and energy in threshold graphs. Linear Algebra Appl. 465, 412\u2013425 (2015)","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"454_CR35","doi-asserted-by":"publisher","first-page":"837","DOI":"10.22199\/issn.0717-6279-2019-04-0055","volume":"38","author":"SK Vaidya","year":"2019","unstructured":"Vaidya, S.K., Popat, K.M.: Construction of sequences of borderenergetic graphs. Proyecciones (Antofagasta) 38(4), 837\u2013847 (2019)","journal-title":"Proyecciones (Antofagasta)"},{"key":"454_CR36","first-page":"37","volume":"77","author":"F Tura","year":"2017","unstructured":"Tura, F.: L-borderenergetic graphs. MATCH Commun. Math. Comput. Chem 77, 37\u201344 (2017)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"issue":"1","key":"454_CR37","first-page":"115","volume":"77","author":"B Deng","year":"2017","unstructured":"Deng, B., Li, X.: More on L-borderenergetic graphs. MATCH Commun. Math. Comput. Chem 77(1), 115\u2013127 (2017)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"issue":"6","key":"454_CR38","first-page":"1237","volume":"40","author":"M Hakimi-Nezhaad","year":"2019","unstructured":"Hakimi-Nezhaad, M., Ghorbani, M.: Laplacian borderenergetic graphs. J. Inf. Optim. Sci. 40(6), 1237\u20131264 (2019)","journal-title":"J. Inf. Optim. Sci."},{"issue":"9","key":"454_CR39","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.3842\/umzh.v75i9.7243","volume":"75","author":"C Dede","year":"2023","unstructured":"Dede, C., Maden, A.D.: Bounds on the parameters of non-L-borderenergetic graphs. Ukrains\u2019 kyi Matematychnyi Zhurnal 75(9), 1220\u20131236 (2023)","journal-title":"Ukrains\u2019 kyi Matematychnyi Zhurnal"},{"issue":"3","key":"454_CR40","first-page":"597","volume":"86","author":"C Dede","year":"2021","unstructured":"Dede, C., Maden, A.D.: Garden of Laplacian borderenergetic graphs. MATCH Commun. Math. Comput. Chem 86(3), 597\u2013610 (2021)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"key":"454_CR41","doi-asserted-by":"publisher","first-page":"729","DOI":"10.46793\/match.90-3.729L","volume":"90","author":"Q Lia","year":"2023","unstructured":"Lia, Q., Tanga, L.: Infinite numbers of infinite classes L-borderenergetic graphs. MATCH Commun. Math. Comput. Chem 90, 729\u2013742 (2023)","journal-title":"MATCH Commun. Math. Comput. Chem"},{"key":"454_CR42","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/0024-3795(94)90486-3","volume":"197","author":"R Merris","year":"1994","unstructured":"Merris, R.: Laplacian matrices of graphs: a survey. Linear Algebra Appl. 197, 143\u2013176 (1994)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"454_CR43","doi-asserted-by":"publisher","first-page":"39","DOI":"10.2298\/AADM150218006B","volume":"9","author":"S Barik","year":"2015","unstructured":"Barik, S., Bapat, R.B., Pati, S.: On the Laplacian spectra of product graphs. Appl. Anal. Discret. Math. 9(1), 39\u201358 (2015)","journal-title":"Appl. Anal. Discret. Math."},{"issue":"2","key":"454_CR44","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1080\/03081088508817681","volume":"18","author":"WN Anderson Jr","year":"1985","unstructured":"Anderson, W.N., Jr., Morley, T.D.: Eigenvalues of the Laplacian of a graph. Linear Multilinear Algebra 18(2), 141\u2013145 (1985)","journal-title":"Linear Multilinear Algebra"}],"container-title":["Acta Informatica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-024-00454-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00236-024-00454-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00236-024-00454-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T06:05:02Z","timestamp":1715666702000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00236-024-00454-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,26]]},"references-count":44,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["454"],"URL":"https:\/\/doi.org\/10.1007\/s00236-024-00454-y","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3239580\/v1","asserted-by":"object"}]},"ISSN":["0001-5903","1432-0525"],"issn-type":[{"value":"0001-5903","type":"print"},{"value":"1432-0525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,26]]},"assertion":[{"value":"6 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}