{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:10Z","timestamp":1753882150271,"version":"3.41.2"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> The aim of this paper is to present a study of the Moore\u2013Penrose inverse [Formula: see text] of the Laplacian matrix of a simple and connected graph, particularly, for some families of graphs such as path, cycle, ladder, fan and wheel graphs. For this purpose, it is used diverse approaches and MP inverse of the Cartesian product of graphs, and are obtained new closed-form formulas of the [Formula: see text] of these families. A comparison of the computational efficiency of the new formulas versus traditional mathematical software is presented, showing the advantage of new formulas. <\/jats:p>","DOI":"10.1142\/s1793830922501397","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T04:19:30Z","timestamp":1660709970000},"source":"Crossref","is-referenced-by-count":0,"title":["A note on Moore\u2013Penrose inverse of Laplacian matrix of graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Luis Carlos Picon","family":"Nu\u00f1ez","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tennessee, Knoxville, TN, USA"}]},{"given":"M. A. C.","family":"Candezano","sequence":"additional","affiliation":[{"name":"Mathematics Department, Universidad del Atl\u00e1ntico, Barranquilla, Colombia"}]}],"member":"219","published-online":{"date-parts":[[2022,10,17]]},"reference":[{"key":"S1793830922501397BIB001","volume-title":"Generalized Inverses: Theory and Applications","author":"Ben-Israel A.","year":"1974","edition":"2"},{"issue":"3","key":"S1793830922501397BIB002","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/TKDE.2007.46","volume":"19","author":"Fouss F.","year":"2007","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"1","key":"S1793830922501397BIB003","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1137\/050645452","volume":"50","author":"Ghosh A.","year":"2008","journal-title":"SIAM Rev."},{"volume-title":"Topics in Matrix Analysis","year":"1994","author":"Horn R. A.","key":"S1793830922501397BIB004"},{"issue":"4","key":"S1793830922501397BIB005","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1137\/S0895479896298713","volume":"18","author":"Kirkland S.","year":"1997","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"1","key":"S1793830922501397BIB006","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":"17","key":"S1793830922501397BIB008","doi-asserted-by":"crossref","first-page":"3833","DOI":"10.1016\/j.physa.2013.04.013","volume":"392","author":"Ranjan G.","year":"2013","journal-title":"Phys. A"},{"key":"S1793830922501397BIB009","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/978-3-319-12691-3_54","volume-title":"Combinatorial Optimization and Applications","author":"Ranjan G.","year":"2014"},{"issue":"4","key":"S1793830922501397BIB010","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1007\/s00214-003-0460-4","volume":"110","author":"Xiao W.","year":"2003","journal-title":"Theor. Chem. Acc."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501397","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T08:40:44Z","timestamp":1686213644000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501397"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,17]]},"references-count":9,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1142\/S1793830922501397"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501397","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,10,17]]},"article-number":"2250139"}}