{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:38:12Z","timestamp":1753886292040,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,10,9]],"date-time":"2012-10-09T00:00:00Z","timestamp":1349740800000},"content-version":"vor","delay-in-days":282,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Let  be the characteristic polynomial of the Laplacian matrix of a graph <jats:italic>G<\/jats:italic> of order <jats:italic>n<\/jats:italic>. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients <jats:italic>c<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) and investigate a conjecture A. Ili\u0107 and M. Ili\u0107 (2009) about the Laplacian coefficients of unicyclic graphs with <jats:italic>n<\/jats:italic> vertices and <jats:italic>m<\/jats:italic> pendent vertices. Finally, we determine the graph with the smallest Laplacian\u2010like energy among all the unicyclic graphs with <jats:italic>n<\/jats:italic> vertices and <jats:italic>m<\/jats:italic> pendent vertices.<\/jats:p>","DOI":"10.1155\/2012\/404067","type":"journal-article","created":{"date-parts":[[2012,10,10]],"date-time":"2012-10-10T17:05:30Z","timestamp":1349888730000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Laplacian Coefficients and Laplacian\u2010Like Energy of Unicyclic Graphs with <i>n<\/i> Vertices and <i>m<\/i> Pendent Vertices"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xinying","family":"Pai","sequence":"first","affiliation":[]},{"given":"Sanyang","family":"Liu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,10,9]]},"reference":[{"volume-title":"Spectra of Graphs-Theory and Applications","year":"1995","author":"Cvetkovi\u0107 D. 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