{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T13:56:17Z","timestamp":1752674177174,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11126256","ZR2012AQ022"],"award-info":[{"award-number":["11126256","ZR2012AQ022"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Shandong Province of China","award":["11126256","ZR2012AQ022"],"award-info":[{"award-number":["11126256","ZR2012AQ022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"LetD<\/mml:mi><\/mml:mrow><\/mml:math>denote the distance matrix of a connected graphG<\/mml:mi><\/mml:mrow><\/mml:math>. The inertia ofD<\/mml:mi><\/mml:mrow><\/mml:math>is the triple of integers (n<\/mml:mi><\/mml:mrow>+<\/mml:mo><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo>,<\/mml:mo>\u00a0<\/mml:mi>n<\/mml:mi><\/mml:mrow>0<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo>,<\/mml:mo>\u00a0<\/mml:mi>n<\/mml:mi><\/mml:mrow>-<\/mml:mo><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo><\/mml:math>), wheren<\/mml:mi><\/mml:mrow>+<\/mml:mo><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo><\/mml:math>,n<\/mml:mi><\/mml:mrow>0<\/mml:mn><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo><\/mml:math>, andn<\/mml:mi><\/mml:mrow>-<\/mml:mo><\/mml:mrow><\/mml:msub>(<\/mml:mo>D<\/mml:mi>)<\/mml:mo><\/mml:math>denote the number of positive, 0, and negative eigenvalues ofD<\/mml:mi><\/mml:mrow><\/mml:math>, respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.<\/jats:p>","DOI":"10.1155\/2013\/707954","type":"journal-article","created":{"date-parts":[[2013,6,15]],"date-time":"2013-06-15T17:00:19Z","timestamp":1371315619000},"page":"1-5","source":"Crossref","is-referenced-by-count":1,"title":["The Distance Matrices of Some Graphs Related to Wheel Graphs"],"prefix":"10.1155","volume":"2013","author":[{"given":"Xiaoling","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengyuan","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"first-page":"295","volume-title":"The role of the topological distance matrix in chemistry","year":"1986","key":"13"},{"key":"4","doi-asserted-by":"crossref","first-page":"2716","DOI":"10.1063\/1.438630","volume":"71","year":"1979","journal-title":"Journal of Chemical Physics"},{"key":"11","first-page":"219","volume":"3","year":"1977","journal-title":"Ars Combinatoria"},{"volume-title":"String edits and macromolecules","year":"1983","key":"1"},{"key":"5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0022-2496(73)90011-4","volume":"10","year":"1973","journal-title":"Journal of Mathematical Psychology"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0070375"},{"key":"14","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1093\/nar\/12.1Part1.237","volume":"12","year":"1984","journal-title":"Nucleic Acids Research"},{"key":"10","doi-asserted-by":"crossref","first-page":"2495","DOI":"10.1002\/j.1538-7305.1971.tb02618.x","volume":"50","year":"1971","journal-title":"The Bell System Technical Journal"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.05.011"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.540110706"},{"volume":"36","year":"1988","key":"6"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.2298\/PIM0999039R"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2013.04.013"},{"volume":"87","first-page":"368","year":"1980","key":"7"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010116"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/707954.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/707954.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/707954.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T10:44:14Z","timestamp":1498041854000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/707954\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":15,"alternative-id":["707954","707954"],"URL":"https:\/\/doi.org\/10.1155\/2013\/707954","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}