{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T14:40:28Z","timestamp":1780065628818,"version":"3.54.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T00:00:00Z","timestamp":1550534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Comb Optim"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s10878-019-00391-4","type":"journal-article","created":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T13:45:35Z","timestamp":1550583935000},"page":"421-442","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On the extremal cacti of given parameters with respect to the difference of zagreb indices"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6856-0827","authenticated-orcid":false,"given":"Shuchao","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Licheng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minjie","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,2,19]]},"reference":[{"issue":"2","key":"391_CR1","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1017\/S0004972715000386","volume":"92","author":"MQ An","year":"2015","unstructured":"An MQ, Xiong LM (2015) Some results on the difference of the Zagreb indices of a graph. Bull Aust Math Soc 92(2):177\u2013186","journal-title":"Bull Aust Math Soc"},{"key":"391_CR2","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/BFb0111212","volume":"114","author":"AT Balaban","year":"1983","unstructured":"Balaban AT, Motoc I, Bonchev D, Mekenyan O (1983) Topological indices for structure-activity correlations. Top Curr Chem 114:21\u201355","journal-title":"Top Curr Chem"},{"key":"391_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph theory","author":"JA Bondy","year":"2008","unstructured":"Bondy JA, Murty USR (2008) Graph theory. Springer, Springer GTM 244"},{"key":"391_CR4","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.amc.2016.01.017","volume":"279","author":"B Borovi\u0107anin","year":"2016","unstructured":"Borovi\u0107anin B, Furtula B (2016) On extremal Zagreb indices of trees with given domination number. Appl Math Comput 279:208\u2013218","journal-title":"Appl Math Comput"},{"key":"391_CR5","first-page":"17","volume":"78","author":"B Borovi\u0107anin","year":"2017","unstructured":"Borovi\u0107anin B, Das KCh, Furtula B, Gutman I (2017) Bounds for Zagreb indices. MATCH Commun Math Comput Chem 78:17\u2013100","journal-title":"MATCH Commun Math Comput Chem"},{"key":"391_CR6","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0012-365X(99)00206-X","volume":"212","author":"G Caporossi","year":"2000","unstructured":"Caporossi G, Hansen P (2000) Variable neighborhood search for extremal graphs. 1. The AutoGraphiX system. Discrete Math 212:29\u201344","journal-title":"Discrete Math"},{"key":"391_CR7","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/S0012-365X(03)00311-X","volume":"276","author":"G Caporossi","year":"2004","unstructured":"Caporossi G, Hansen P (2004) Variable neighborhood search for extremal graphs. 5. Three ways to automate finding conjectures. Discrete Math 276:81\u201394","journal-title":"Discrete Math"},{"issue":"2","key":"391_CR8","first-page":"441","volume":"63","author":"G Caporossi","year":"2010","unstructured":"Caporossi G, Hansen P, Vuki\u010devi\u0107 D (2010) Comparing Zagreb indices of cyclic graphs. MATCH Commun Math Comput Chem 63(2):441\u2013451","journal-title":"MATCH Commun Math Comput Chem"},{"issue":"2","key":"391_CR9","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1007\/s10440-009-9467-8","volume":"110","author":"YQ Feng","year":"2010","unstructured":"Feng YQ, Hu X, Li SC (2010) On the extremal Zagreb indices of graphs with cut edges. Acta Appl Math 110(2):667\u2013684","journal-title":"Acta Appl Math"},{"key":"391_CR10","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.dam.2014.06.011","volume":"178","author":"B Furtula","year":"2014","unstructured":"Furtula B, Gutman I, Ediz S (2014) On difference of Zagreb indices. Discrete Appl Math 178:83\u201388","journal-title":"Discrete Appl Math"},{"key":"391_CR11","doi-asserted-by":"publisher","first-page":"351","DOI":"10.5562\/cca2294","volume":"86","author":"I Gutman","year":"2013","unstructured":"Gutman I (2013) Degree-based topological indices. Croat Chem Acta 86:351\u2013361","journal-title":"Croat Chem Acta"},{"key":"391_CR12","first-page":"83","volume":"50","author":"I Gutman","year":"2004","unstructured":"Gutman I, Das KC (2004) The first Zagreb index 30 years after. MATCH Commun Math Comput Chem 50:83\u201392","journal-title":"MATCH Commun Math Comput Chem"},{"key":"391_CR13","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/0009-2614(72)85099-1","volume":"179","author":"I Gutman","year":"1972","unstructured":"Gutman I, Trinajsti\u0107 N (1972) Graph theory and molecular Total orbitals. $$\\pi $$ \u03c0 -electron energy of alternant hydrocarbons. Chem Phys Lett 179:535\u2013538","journal-title":"Chem Phys Lett"},{"key":"391_CR14","doi-asserted-by":"publisher","first-page":"3399","DOI":"10.1063\/1.430994","volume":"62","author":"I Gutman","year":"1975","unstructured":"Gutman I, Ru\u0161\u010di\u0107 B, Trinajsti\u0107 N, Wilcox CF (1975) Graph theory and molecular orbitals. XII. Acyclic polyenes. J Phys Chem 62:3399\u20133405","journal-title":"J Phys Chem"},{"key":"391_CR15","first-page":"165","volume":"80","author":"P Hansen","year":"2007","unstructured":"Hansen P, Vuki\u010devi\u0107 D (2007) Comparing the Zagreb indices. Croat Chem Acta 80:165\u2013168","journal-title":"Croat Chem Acta"},{"key":"391_CR16","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/j.amc.2017.07.067","volume":"315","author":"WH He","year":"2017","unstructured":"He WH, Li H, Xiao SF (2017) On the minimum Kirchhoff index of graphs with a given vertex $$k$$ k -partiteness and edge $$k$$ k -partiteness. Appl Math Comput 315:313\u2013318","journal-title":"Appl Math Comput"},{"key":"391_CR17","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.dam.2016.07.008","volume":"215","author":"B Horoldagva","year":"2016","unstructured":"Horoldagva B, Das KC, Selenge T (2016) Complete characterization of graphs for direct comparing Zagreb indices. Discrete Appl Math 215:146\u2013154","journal-title":"Discrete Appl Math"},{"key":"391_CR18","first-page":"337","volume":"78","author":"B Horoldagva","year":"2017","unstructured":"Horoldagva B, Buyantogtokh L, Dorjsembe S (2017) Difference of Zagreb indices and reduced second Zagreb index of cyclic graphs with cut edges. MATCH Commun Math Comput Chem 78:337\u2013350","journal-title":"MATCH Commun Math Comput Chem"},{"issue":"2","key":"391_CR19","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/s10878-010-9288-8","volume":"22","author":"AL Hou","year":"2011","unstructured":"Hou AL, Li SC, Song LZ, Wei B (2011) Sharp bounds for Zagreb indices of maximal outerplanar graphs. J Comb Optim 22(2):252\u2013269","journal-title":"J Comb Optim"},{"issue":"2","key":"391_CR20","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.aml.2010.08.032","volume":"24","author":"SC Li","year":"2011","unstructured":"Li SC, Zhang MJ (2011) Sharp upper bounds for Zagreb indices of bipartite graphs with a given diameter. Appl Math Lett 24(2):131\u2013137","journal-title":"Appl Math Lett"},{"issue":"11\u201312","key":"391_CR21","doi-asserted-by":"publisher","first-page":"2869","DOI":"10.1016\/j.mcm.2011.07.007","volume":"54","author":"SC Li","year":"2011","unstructured":"Li SC, Zhao Q (2011) Sharp upper bounds on Zagreb indices of bicyclic graphs with a given matching number. Math Comput Model 54(11\u201312):2869\u20132879","journal-title":"Math Comput Model"},{"issue":"2","key":"391_CR22","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.aml.2009.08.015","volume":"23","author":"SC Li","year":"2010","unstructured":"Li SC, Zhou HB (2010) On the maximum and minimum Zagreb indices of graphs with connectivity at most $$k$$ k . Appl Math Lett 23(2):128\u2013132","journal-title":"Appl Math Lett"},{"key":"391_CR23","first-page":"157","volume":"68","author":"M Milo\u0161evi\u0107","year":"2012","unstructured":"Milo\u0161evi\u0107 M, R\u00e9ti T, Stevanovi\u0107 D (2012) On the constant difference of Zagreb indices. MATCH Commun Math Comput Chem 68:157\u2013168","journal-title":"MATCH Commun Math Comput Chem"},{"key":"391_CR24","first-page":"113","volume":"76","author":"S Nikoli\u0107","year":"2003","unstructured":"Nikoli\u0107 S, Kova\u010devi\u0107 G, Mili\u010devi\u0107 A, Trinajsti\u0107 N (2003) The Zagreb indices 30 years after. Croat Chem Acta 76:113\u2013124","journal-title":"Croat Chem Acta"},{"issue":"9","key":"391_CR25","doi-asserted-by":"publisher","first-page":"2575","DOI":"10.1016\/j.disc.2018.06.009","volume":"341","author":"A Sah","year":"2018","unstructured":"Sah A, Sawhney M (2018) On the discrepancy between two Zagreb indices. Discrete Math 341(9):2575\u20132589","journal-title":"Discrete Math"},{"issue":"2","key":"391_CR26","first-page":"351","volume":"78","author":"T-A Selenge","year":"2017","unstructured":"Selenge T-A, Horoldagva B, Das KC (2017) Direct comparison of the variable Zagreb indices of cyclic graphs. MATCH Commun Math Comput Chem 78(2):351\u2013360","journal-title":"MATCH Commun Math Comput Chem"},{"key":"391_CR27","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.dam.2018.03.084","volume":"247","author":"T Vetr\u00edk","year":"2018","unstructured":"Vetr\u00edk T, Balachandran S (2018) General multiplicative Zagreb indices of trees. Discrete Appl Math 247:341\u2013351","journal-title":"Discrete Appl Math"},{"key":"391_CR28","doi-asserted-by":"publisher","first-page":"1212","DOI":"10.1016\/j.disc.2015.11.013","volume":"339","author":"H Wang","year":"2016","unstructured":"Wang H, Yuan S (2016) On the sum of squares of degrees and products of adjacent degrees. Discrete Math 339:1212\u20131220","journal-title":"Discrete Math"},{"key":"391_CR29","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.dam.2014.12.015","volume":"185","author":"WG Yuan","year":"2015","unstructured":"Yuan WG, Zhang XD (2015) The second Zagreb indices of graphs with given degree sequence. Discrete Appl Math 185:230\u2013238","journal-title":"Discrete Appl Math"},{"issue":"17","key":"391_CR30","doi-asserted-by":"publisher","first-page":"1953","DOI":"10.1016\/j.dam.2010.08.005","volume":"158","author":"Q Zhao","year":"2010","unstructured":"Zhao Q, Li SC (2010a) Sharp bounds for the Zagreb indices of bicyclic graphs with $$k$$ k -pendant vertices. Discrete Appl Math 158(17):1953\u20131962","journal-title":"Discrete Appl Math"},{"issue":"1","key":"391_CR31","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/s10440-009-9534-1","volume":"111","author":"Q Zhao","year":"2010","unstructured":"Zhao Q, Li SC (2010b) On the maximum Zagreb indices of graphs with $$k$$ k cut vertices. Acta Appl Math 111(1):93\u2013106","journal-title":"Acta Appl Math"}],"container-title":["Journal of Combinatorial Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10878-019-00391-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-019-00391-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10878-019-00391-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T03:06:16Z","timestamp":1662951976000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10878-019-00391-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,19]]},"references-count":31,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["391"],"URL":"https:\/\/doi.org\/10.1007\/s10878-019-00391-4","relation":{},"ISSN":["1382-6905","1573-2886"],"issn-type":[{"value":"1382-6905","type":"print"},{"value":"1573-2886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,19]]},"assertion":[{"value":"19 February 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}