{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T11:09:08Z","timestamp":1767092948333,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T00:00:00Z","timestamp":1609891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11861019"],"award-info":[{"award-number":["11861019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Guizhou","award":["[2019]1047","[2020]1Z001"],"award-info":[{"award-number":["[2019]1047","[2020]1Z001"]}]},{"name":"Guizhou Talent Development Project in Science and Technology","award":["KY[2018]046"],"award-info":[{"award-number":["KY[2018]046"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s12190-020-01473-x","type":"journal-article","created":{"date-parts":[[2021,1,6]],"date-time":"2021-01-06T15:08:45Z","timestamp":1609945725000},"page":"89-100","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The average Steiner 3-eccentricity of block graphs"],"prefix":"10.1007","volume":"67","author":[{"given":"Xingfu","family":"Li","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3616-5344","authenticated-orcid":false,"given":"Guihai","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,6]]},"reference":[{"key":"1473_CR1","first-page":"37","volume":"107","author":"P Ali","year":"2018","unstructured":"Ali, P., Dankelmann, P., Morgan, M.J., et al.: The average eccentricity, spanning trees of plane graphs, size and order. Util. Math. 107, 37\u201349 (2018)","journal-title":"Util. Math."},{"key":"1473_CR2","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s00373-011-1031-4","volume":"28","author":"BS Anand","year":"2012","unstructured":"Anand, B.S., Changat, M., Klavzar, S., Peterin, I.: Convex sets in lexicographic product of graphs. Graphs Combin. 28, 77\u201384 (2012)","journal-title":"Graphs Combin."},{"key":"1473_CR3","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/0166-218X(95)00069-4","volume":"68","author":"LW Beineke","year":"1996","unstructured":"Beineke, L.W., Oellermann, O.R., Pippert, R.E.: On the Steiner median of a tree. Discrete Appl. Math. 68, 249\u2013258 (1996)","journal-title":"Discrete Appl. Math."},{"key":"1473_CR4","volume-title":"Distance in Graphs","author":"F Buckley","year":"1990","unstructured":"Buckley, F., Harary, F.: Distance in Graphs. Addisson-Wesley, Redwood City (1990)"},{"key":"1473_CR5","doi-asserted-by":"publisher","first-page":"399","DOI":"10.21136\/CPM.1989.118395","volume":"114","author":"G Chartrand","year":"1989","unstructured":"Chartrand, G., Oellermann, O.R., Tian, S., Zou, H.B.: Steiner distance in graphs. \u0106asopis pro p\u011bst\u00f3vani matematiky 114, 399\u2013410 (1989)","journal-title":"\u0106asopis pro p\u011bst\u00f3vani matematiky"},{"key":"1473_CR6","volume-title":"Introduction to Algorithme","author":"TH Cormen","year":"2001","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithme. MIT Press, Cambridge (2001)"},{"key":"1473_CR7","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/S0166-218X(97)00035-8","volume":"79","author":"P Dankelmann","year":"1997","unstructured":"Dankelmann, P., Swart, H.C., Oellermann, O.R.: The average Steiner distance of graphs with prescribed properties. Discrete Appl. Math. 79, 91\u2013103 (1997)","journal-title":"Discrete Appl. Math."},{"issue":"1","key":"1473_CR8","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1002\/(SICI)1097-0118(199605)22:1<15::AID-JGT3>3.0.CO;2-O","volume":"22","author":"P Dankelmann","year":"1996","unstructured":"Dankelmann, P., Oellermann, O.R., Swart, H.C.: The average Steiner distance of a graph. J. Graph Theory 22(1), 15\u201322 (1996)","journal-title":"J. Graph Theory"},{"key":"1473_CR9","first-page":"41","volume":"65","author":"P Dankelmann","year":"2004","unstructured":"Dankelmann, P., Goddard, W., Swart, C.: The average eccentricity of a graph and its subgraphs. Util. Math. 65, 41\u201351 (2004)","journal-title":"Util. Math."},{"key":"1473_CR10","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/j.dam.2013.11.023","volume":"167","author":"P Dankelmann","year":"2014","unstructured":"Dankelmann, P., Mukwembi, S.: Upper bounds on the average eccentricity. Discrete Appl. Math. 167, 72\u201379 (2014)","journal-title":"Discrete Appl. Math."},{"key":"1473_CR11","doi-asserted-by":"publisher","first-page":"1261","DOI":"10.1016\/j.disc.2019.01.004","volume":"342","author":"P Dankelmann","year":"2019","unstructured":"Dankelmann, P., Osaye, F.J.: Average eccentricity, k-packing and k-domination in graphs. Discrete Math. 342, 1261\u20131274 (2019)","journal-title":"Discrete Math."},{"issue":"1","key":"1473_CR12","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.dam.2019.06.003","volume":"270","author":"P Dankelmann","year":"2019","unstructured":"Dankelmann, P., Osaye, F.J., Mukwembi, S., Rodrigues, B.: Upper bounds on the average eccentricity of K3-free and C4-free graphs. Discrete Appl. Math. 270(1), 106\u2013114 (2019)","journal-title":"Discrete Appl. Math."},{"key":"1473_CR13","first-page":"597","volume":"69","author":"Z Du","year":"2013","unstructured":"Du, Z., Ili\u0107, A.: On AGX conjectures regarding average eccentricity. MATCH Commun. Math. Comput. Chem. 69, 597\u2013609 (2013)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"1473_CR14","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/j.dam.2015.08.002","volume":"201","author":"Z Du","year":"2016","unstructured":"Du, Z., Ili\u0107, A.: A proof of the conjecture regarding the sum of the domination number and average eccentricity. Discrete Appl. Math. 201, 105\u2013113 (2016)","journal-title":"Discrete Appl. Math."},{"key":"1473_CR15","volume-title":"Computers and Intractibility: A Guide to the Theory of NP-Completeness","author":"MR Garey","year":"1979","unstructured":"Garey, M.R., Johnson, D.S.: Computers and Intractibility: A Guide to the Theory of NP-Completeness. Freeman & Company, New York (1979)"},{"key":"1473_CR16","first-page":"733","volume":"82","author":"M Ghorbani","year":"2019","unstructured":"Ghorbani, M., Li, X., Maimani, H.R., Mao, Y., Rahmani, S., Parsa, M.R.: Steiner (revised) Szeged index of graphs. MATCH Commun. Math. Comput. Chem. 82, 733\u2013742 (2019)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"1473_CR17","first-page":"627","volume":"41","author":"T Gologranc","year":"2018","unstructured":"Gologranc, T.: Steiner convex sets and Cartesian product. Bull. Malays. Math. Sci. Soc. 41, 627\u2013636 (2018)","journal-title":"Bull. Malays. Math. Sci. Soc."},{"issue":"1","key":"1473_CR18","doi-asserted-by":"publisher","first-page":"83","DOI":"10.7151\/dmgt.2000","volume":"38","author":"I Gutman","year":"2017","unstructured":"Gutman, I., Li, X., Mao, Y.: Inverse problem on the Steiner Wiener index. Discuss. Math. Graph Theory 38(1), 83\u201395 (2017)","journal-title":"Discuss. Math. Graph Theory"},{"key":"1473_CR19","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.amc.2016.02.038","volume":"283","author":"I Gutman","year":"2016","unstructured":"Gutman, I.: On Steiner degree distance of trees. Appl. Math. Comput. 283, 163\u2013167 (2016)","journal-title":"Appl. Math. Comput."},{"key":"1473_CR20","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.2298\/JSC150126015G","volume":"80","author":"I Gutman","year":"2015","unstructured":"Gutman, I., Furtula, B., Li, X.: Multicenter Wiener indices and their applications. J. Serb. Chem. Soc. 80, 1009\u20131017 (2015)","journal-title":"J. Serb. Chem. Soc."},{"key":"1473_CR21","volume-title":"The Steiner Tree Problem","author":"FK Hwang","year":"1992","unstructured":"Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem, vol. 53. North-Holland, Amsterdam (1992)"},{"issue":"9","key":"1473_CR22","doi-asserted-by":"publisher","first-page":"2877","DOI":"10.1016\/j.camwa.2012.04.023","volume":"64","author":"A Ili\u0107","year":"2012","unstructured":"Ili\u0107, A.: On the extremal properties of the average eccentricity. Comput. Math. Appl. 64(9), 2877\u20132885 (2012)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"1473_CR23","doi-asserted-by":"publisher","first-page":"455","DOI":"10.7151\/dmgt.1868","volume":"36","author":"X Li","year":"2016","unstructured":"Li, X., Mao, Y., Gutman, I.: The Steiner Wiener index of a graph. Discuss. Math. Graph Theory 36(2), 455\u2013465 (2016)","journal-title":"Discuss. Math. Graph Theory"},{"key":"1473_CR24","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1016\/j.disc.2017.11.009","volume":"341","author":"L Lu","year":"2018","unstructured":"Lu, L., Huang, Q., Hou, J., Chen, X.: A sharp lower bound on the Steiner Wiener index for trees with given diameter. Discrete Math. 341, 723\u2013731 (2018)","journal-title":"Discrete Math."},{"issue":"3","key":"1473_CR25","first-page":"779","volume":"79","author":"Y Mao","year":"2018","unstructured":"Mao, Y., Das, K.C.: Steiner Gutman index. MATCH Commun. Math. Comput. Chem. 79(3), 779\u2013794 (2018)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"unstructured":"Mao, Y.: Steiner Distance in Graphs\u2014A Survey. arXiv:1708.05779 (2017)","key":"1473_CR26"},{"doi-asserted-by":"publisher","unstructured":"Mao, Y., Cheng, E., Wang, Z.: Steiner distance in product networks. Discrete Math. Theor. Comput. Sci. 20(2), 8 (2018). https:\/\/doi.org\/10.23638\/DMTCS-20-2-8","key":"1473_CR27","DOI":"10.23638\/DMTCS-20-2-8"},{"key":"1473_CR28","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.dam.2016.02.013","volume":"207","author":"H Smith","year":"2016","unstructured":"Smith, H., Sz\u00e9kely, L.A., Wang, H.: Eccentricity sum in trees. Discrete Appl. Math. 207, 120\u2013131 (2016)","journal-title":"Discrete Appl. Math."},{"key":"1473_CR29","first-page":"405","volume":"67","author":"Y Tang","year":"2012","unstructured":"Tang, Y., Zhou, B.: On average eccentricity. MATCH Commun. Math. Comput. Chem. 67, 405\u2013423 (2012)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"issue":"15","key":"1473_CR30","first-page":"360","volume":"337","author":"N Tratnik","year":"2019","unstructured":"Tratnik, N.: On the Steiner hyper-Wiener index of a graph. Appl. Math. Comput. 337(15), 360\u2013371 (2019)","journal-title":"Appl. Math. Comput."},{"doi-asserted-by":"crossref","unstructured":"Wang, Z., Mao, Y., Melekian, C., Cheng, E.: Steiner distance in join, corona, and threshold graphs. In: The 14th International Symposium on Pervasive Systems. Algorithms and Networks (2017). https:\/\/doi.org\/10.1109\/ISPAN-FCST-ISCC.2017.39","key":"1473_CR31","DOI":"10.1109\/ISPAN-FCST-ISCC.2017.39"},{"issue":"5","key":"1473_CR32","doi-asserted-by":"publisher","first-page":"4459","DOI":"10.3934\/math.2020286","volume":"5","author":"M Wei","year":"2020","unstructured":"Wei, M., Yue, J., Zhu, X.: On the edge metric dimension of graphs. AIMS Math. 5(5), 4459\u20134465 (2020)","journal-title":"AIMS Math."},{"key":"1473_CR33","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1016\/j.dam.2018.02.003","volume":"243","author":"J Yue","year":"2017","unstructured":"Yue, J., Lei, H., Shi, Y.: On the generalized Wiener polarity index of trees with a given diameter. Discrete Appl. Math. 243, 279\u2013285 (2017)","journal-title":"Discrete Appl. Math."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01473-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01473-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01473-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,10]],"date-time":"2022-12-10T19:54:10Z","timestamp":1670702050000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01473-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,6]]},"references-count":33,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1473"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01473-x","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2021,1,6]]},"assertion":[{"value":"28 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 January 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}