{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:46:28Z","timestamp":1757619988469,"version":"3.44.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T00:00:00Z","timestamp":1753660800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T00:00:00Z","timestamp":1753660800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12061073"],"award-info":[{"award-number":["12061073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2025,8]]},"DOI":"10.1007\/s00373-025-02951-4","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T10:19:14Z","timestamp":1753697954000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Neighbor sum distinguishing index of $$K_4$$-minor free graphs"],"prefix":"10.1007","volume":"41","author":[{"given":"Wei","family":"Yang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7164-3116","authenticated-orcid":false,"given":"Baoyindureng","family":"Wu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"2951_CR1","doi-asserted-by":"publisher","first-page":"3005","DOI":"10.1016\/j.disc.2004.12.027","volume":"306","author":"S Akbari","year":"2006","unstructured":"Akbari, S., Bidkhori, H., Nosrati, N.: $$r$$-Strong edge colorings of graphs. Discrete Math. 306, 3005\u20133010 (2006)","journal-title":"Discrete Math."},{"key":"2951_CR2","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1137\/S0895480102414107","volume":"21","author":"PN Balister","year":"2007","unstructured":"Balister, P.N., Gy\u0151ri, E., Lehel, J., Schelp, R.H.: Adjacent vertex distinguishing edge-colorings. SIAM J. Discrete Math. 21, 237\u2013250 (2007)","journal-title":"SIAM J. Discrete Math."},{"issue":"3","key":"2951_CR3","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1002\/jgt.22098","volume":"85","author":"M Bonamy","year":"2017","unstructured":"Bonamy, M., Przyby\u0142o, J.: On the neighbor sum distinguishing index of planar graphs. J. Graph Theory 85(3), 669\u2013690 (2017)","journal-title":"J. Graph Theory"},{"key":"2951_CR4","volume-title":"Graph Theory, Graduate Text in Mathematics","author":"JA Bondy","year":"2008","unstructured":"Bondy, J.A., Murty, U.S.R.: Graph Theory, Graduate Text in Mathematics, vol. 244. Springer, New York (2008)"},{"issue":"3","key":"2951_CR5","doi-asserted-by":"publisher","first-page":"429","DOI":"10.7151\/dmgt.1556","volume":"31","author":"Y Bu","year":"2011","unstructured":"Bu, Y., Lih, K., Wang, W.: Adjacent vertex distinguishing edge-colorings of planar graphs with girth at least six. Disc. Math. Graph Theory 31(3), 429\u2013439 (2011)","journal-title":"Disc. Math. Graph Theory"},{"issue":"4","key":"2951_CR6","doi-asserted-by":"publisher","first-page":"1250047","DOI":"10.1142\/S1793830912500474","volume":"4","author":"A Dong","year":"2012","unstructured":"Dong, A., Wang, G.: Neighbor sum distinguishing colorings of some graphs. Discrete Math. Algorithms Appl. 4(4), 1250047 (2012)","journal-title":"Discrete Math. Algorithms Appl."},{"key":"2951_CR7","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/0022-247X(65)90125-3","volume":"10","author":"J Duffin","year":"1965","unstructured":"Duffin, J.: Topology of series-parallel networks. J. Math. Anal. Appl. 10, 303\u2013318 (1965)","journal-title":"J. Math. Anal. Appl."},{"key":"2951_CR8","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s00373-006-0671-2","volume":"22","author":"K Edwards","year":"2006","unstructured":"Edwards, K., Hor\u0148\u00e1k, M., Wozniak, M.: On the neighbour-distinguishing index of a graph. Graphs Comb. 22, 341\u2013350 (2006)","journal-title":"Graphs Comb."},{"key":"2951_CR9","doi-asserted-by":"publisher","first-page":"1329","DOI":"10.1007\/s00373-012-1191-x","volume":"29","author":"E Flandrin","year":"2013","unstructured":"Flandrin, E., Marczyk, A., Przyby\u0142o, J., Sacl\u00e9, J., Wozniak, M.: Neighbor sum distinguishing index. Graphs Combin. 29, 1329\u20131336 (2013)","journal-title":"Graphs Combin."},{"issue":"1","key":"2951_CR10","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/s10878-011-9444-9","volume":"26","author":"H Hocquard","year":"2013","unstructured":"Hocquard, H., Montassier, M.: Adjacent vertex-distinguishing edge coloring of graphs with maximum degree $$\\Delta $$. J. Comb. Optim. 26(1), 152\u2013160 (2013)","journal-title":"J. Comb. Optim."},{"issue":"4","key":"2951_CR11","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1002\/jgt.21764","volume":"76","author":"M Hor\u0148\u00e1k","year":"2014","unstructured":"Hor\u0148\u00e1k, M., Huang, D., Wang, W.: On neighbor-distinguishing index of planar graphs. J. Graph Theory 76(4), 262\u2013278 (2014)","journal-title":"J. Graph Theory"},{"key":"2951_CR12","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.ejc.2018.10.009","volume":"77","author":"J Przyby\u0142o","year":"2019","unstructured":"Przyby\u0142o, J.: A note on asymptotically optimal neighbour sum distinguishing colourings. European J. Combin. 77, 49\u201356 (2019)","journal-title":"European J. Combin."},{"key":"2951_CR13","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.disc.2014.06.027","volume":"334","author":"G Wang","year":"2014","unstructured":"Wang, G., Chen, Z., Wang, J.: Neighbor sum distinguishing index of planar graphs. Discrete Math. 334, 70\u201373 (2014)","journal-title":"Discrete Math."},{"key":"2951_CR14","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s10878-008-9178-5","volume":"19","author":"W Wang","year":"2010","unstructured":"Wang, W., Wang, Y.: Adjacent vertex distinguishing edge-colorings of graphs with smaller maximum average degree. J. Comb. Optim. 19, 471\u2013485 (2010)","journal-title":"J. Comb. Optim."},{"issue":"12","key":"2951_CR15","doi-asserted-by":"publisher","first-page":"2034","DOI":"10.1016\/j.aml.2011.05.038","volume":"24","author":"W Wang","year":"2011","unstructured":"Wang, W., Wang, Y.: Adjacent vertex-distinguishing edge colorings of $$K_4$$-minor free graphs. Appl. Math. Lett. 24(12), 2034\u20132037 (2011)","journal-title":"Appl. Math. Lett."},{"key":"2951_CR16","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.ipl.2017.09.007","volume":"129","author":"Y Wang","year":"2018","unstructured":"Wang, Y., Wang, P., Wang, W.: Strong chromatic index of $$K_4$$-minor free graphs. Inf. Process. Lett. 129, 53\u201356 (2018)","journal-title":"Inf. Process. Lett."},{"key":"2951_CR17","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.dam.2014.05.013","volume":"175","author":"G Wang","year":"2014","unstructured":"Wang, G., Yan, G.: An improved upper bound for the neighbor sum distinguishing index of graphs. Discrete Appl. Math. 175, 126\u2013128 (2014)","journal-title":"Discrete Appl. Math."},{"key":"2951_CR18","doi-asserted-by":"publisher","first-page":"1621","DOI":"10.1007\/s00373-015-1655-x","volume":"32","author":"J Zhang","year":"2016","unstructured":"Zhang, J., Ding, L., Wang, G., Yan, G., Zhou, S.: Neighbor sum distinguishing index of $$K_4$$-minor free graphs. Graphs Combin. 32, 1621\u20131633 (2016)","journal-title":"Graphs Combin."},{"key":"2951_CR19","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1016\/S0893-9659(02)80015-5","volume":"15","author":"Z Zhang","year":"2002","unstructured":"Zhang, Z., Liu, L., Wang, J.: Adjacent strong edge coloring of graphs. J. Appl. Math. Lett. 15, 623\u2013626 (2002)","journal-title":"J. Appl. Math. Lett."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02951-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-02951-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02951-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T04:19:58Z","timestamp":1757305198000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-02951-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,28]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2951"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-02951-4","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2025,7,28]]},"assertion":[{"value":"28 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have not disclosed any Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"90"}}