{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:08Z","timestamp":1753882148720,"version":"3.41.2"},"reference-count":18,"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> In this paper, we construct a weighted [Formula: see text]-simplicial complex [Formula: see text] on a connected oriented locally finite graph [Formula: see text] by the introduction of the notion of oriented tetrahedrons [Formula: see text], the notion of oriented triangular faces [Formula: see text], a weight on [Formula: see text], a weight on [Formula: see text], a weight on [Formula: see text] and a weight on [Formula: see text]. Next, we create the weighted Gauss\u2013Bonnet operator of [Formula: see text] and we use it to construct the weighted Laplacian associated to [Formula: see text], the weighted Laplacian associated to [Formula: see text], the weighted Laplacian associated to [Formula: see text], the weighted Laplacian associated to [Formula: see text] and the weighted Laplacian associated to [Formula: see text]. After that, we introduce the notion of the [Formula: see text]-completeness of [Formula: see text] and we give necessary conditions for [Formula: see text] to be [Formula: see text]-complete. Finally, we prove that the weighted Gauss\u2013Bonnet operator and the weighted Laplacians are essentially self-adjoint based on the [Formula: see text]-completeness. <\/jats:p>","DOI":"10.1142\/s1793830922501348","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":["Essential self-adjointness of a weighted 3-simplicial complex Laplacians"],"prefix":"10.1142","volume":"15","author":[{"given":"Azeddine","family":"Baalal","sequence":"first","affiliation":[{"name":"Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences A\u00efn Chock, Hassan II, University of Casablanca, Morocco"}]},{"given":"Khalid","family":"Hatim","sequence":"additional","affiliation":[{"name":"Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences A\u00efn Chock, Hassan II, University of Casablanca, Morocco"}]}],"member":"219","published-online":{"date-parts":[[2022,10,17]]},"reference":[{"issue":"2","key":"S1793830922501348BIB001","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s13324-014-0090-0","volume":"5","author":"Ann\u00e9 C.","year":"2015","journal-title":"Anal. 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