{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T02:07:22Z","timestamp":1762999642128,"version":"3.37.3"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61977016"],"award-info":[{"award-number":["61977016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61572010"],"award-info":[{"award-number":["61572010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2017J01738"],"award-info":[{"award-number":["2017J01738"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["JAT170118"],"award-info":[{"award-number":["JAT170118"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["JT180077"],"award-info":[{"award-number":["JT180077"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Parallel Process. Lett."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> The Shapley distance in a graph is defined based on Shapley value in cooperative game theory. It is used to measure the cost for a vertex in a graph to access another vertex. In this paper, we establish the Shapley distance between two arbitrary vertices for some special graphs, i.e., path, tree, cycle, complete graph, complete bipartite, and complete multipartite graph. Moreover, based on the Shapley distance, we propose a new index, namely Shapley index, and then compare Shapley index with Wiener index and Kirchhoff index for these special graphs. We also characterize the extremal graphs in which these three indices are equal. <\/jats:p>","DOI":"10.1142\/s0129626420500127","type":"journal-article","created":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T09:47:13Z","timestamp":1610012833000},"page":"2050012","source":"Crossref","is-referenced-by-count":7,"title":["Shapley Distance and Shapley Index for Some Special Graphs"],"prefix":"10.1142","volume":"30","author":[{"given":"Zhendong","family":"Gu","sequence":"first","affiliation":[{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian, 350117, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6481-3981","authenticated-orcid":false,"given":"Shuming","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian, 350117, P. R. China"},{"name":"Center for Applied Mathematics of Fujian Province (Fujian Normal University), Fuzhou, Fujian 350117, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiafei","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian, 350117, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianru","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Mathematics and Informatics, Fujian Normal University, Fuzhou, Fujian, 350117, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dajin","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Montclair State University, Upper Montclair, NJ 07043, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"S0129626420500127BIB001","series-title":"Ann. of Math. Studies","volume-title":"Contributions to the Theory of Games II","volume":"28","author":"Shapley L.","year":"1953"},{"key":"S0129626420500127BIB002","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1016\/j.physa.2017.08.111","volume":"491","author":"Jonnalagadda A.","year":"2018","journal-title":"Phys. A"},{"issue":"2","key":"S0129626420500127BIB003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3235026","volume":"10","author":"Skibski O.","year":"2019","journal-title":"ACM Trans. Intell. Syst. Technol."},{"issue":"1","key":"S0129626420500127BIB004","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1109\/TASE.2010.2052042","volume":"8","author":"Narayanam R.","year":"2011","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"issue":"2","key":"S0129626420500127BIB005","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1080\/03081079.2018.1549550","volume":"48","author":"Tang J.","year":"2019","journal-title":"Int. J. Gen. Syst."},{"key":"S0129626420500127BIB006","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.trb.2017.08.029","volume":"105","author":"Hadas Y.","year":"2017","journal-title":"Transp. Res. Part B"},{"issue":"2","key":"S0129626420500127BIB007","first-page":"1369","volume":"32","author":"Sharma S.","year":"2017","journal-title":"IEEE Trans. Power Syst."},{"issue":"9","key":"S0129626420500127BIB008","doi-asserted-by":"crossref","first-page":"3290","DOI":"10.1109\/TCOMM.2015.2458319","volume":"63","author":"Immink K. A. Schouhamer","year":"2015","journal-title":"IEEE Trans. Commun."},{"issue":"11","key":"S0129626420500127BIB009","first-page":"1159","volume":"29","author":"Jayanth S.","year":"2006","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"S0129626420500127BIB010","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.ins.2017.03.036","volume":"403","author":"Li T.","year":"2017","journal-title":"Inf. Sci."},{"issue":"1","key":"S0129626420500127BIB011","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1109\/TASLP.2013.2285474","volume":"22","author":"Senoussaoui M.","year":"2014","journal-title":"IEEE\/ACM Trans. Audio, Speech, Lang. Process."},{"key":"S0129626420500127BIB012","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.ins.2017.10.054","volume":"432","author":"Gallardo J. M.","year":"2018","journal-title":"Inf. Sci."},{"key":"S0129626420500127BIB013","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1021\/ja01193a005","volume":"69","author":"Wiener H.","year":"1947","journal-title":"J. Am. Chem. Soc."},{"issue":"1","key":"S0129626420500127BIB014","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/qua.560500102","volume":"50","author":"Bonchev D.","year":"1994","journal-title":"Int. J. Quantum Chem."},{"key":"S0129626420500127BIB015","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph Theory","volume":"244","author":"Bondy J. A.","year":"2008"},{"key":"S0129626420500127BIB016","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01164627","volume":"12","author":"Klein D. J.","year":"1993","journal-title":"J. Math. Chem."},{"issue":"3","key":"S0129626420500127BIB017","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/(SICI)1097-461X(1999)71:3<217::AID-QUA1>3.0.CO;2-C","volume":"71","author":"Lukovits I.","year":"1999","journal-title":"Int. J. Quantum Chem."},{"issue":"2","key":"S0129626420500127BIB018","first-page":"633","volume":"75","author":"Klein D. J.","year":"2002","journal-title":"Croat. Chem. Acta"},{"key":"S0129626420500127BIB019","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.dam.2015.09.017","volume":"203","author":"Gervacio S. V.","year":"2016","journal-title":"Discret. Appl. Math."},{"key":"S0129626420500127BIB020","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1023\/A:1010767517079","volume":"66","author":"Dobrynin A. A.","year":"2001","journal-title":"Acta Appl. Math."}],"container-title":["Parallel Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129626420500127","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T09:48:37Z","timestamp":1610012917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129626420500127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":20,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1142\/S0129626420500127"],"URL":"https:\/\/doi.org\/10.1142\/s0129626420500127","relation":{},"ISSN":["0129-6264","1793-642X"],"issn-type":[{"type":"print","value":"0129-6264"},{"type":"electronic","value":"1793-642X"}],"subject":[],"published":{"date-parts":[[2020,12]]}}}