{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T16:13:21Z","timestamp":1783095201479,"version":"3.54.6"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T00:00:00Z","timestamp":1543708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2017M621579"],"award-info":[{"award-number":["2017M621579"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010246","name":"Postdoctoral Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["1701081B"],"award-info":[{"award-number":["1701081B"]}],"id":[{"id":"10.13039\/501100010246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The methods of measuring the complexity (spanning trees) in a finite graph, a problem related to various areas of mathematics and physics, have been inspected by many mathematicians and physicists. In this work, we defined some classes of pyramid graphs created by a gear graph then we developed the Kirchhoff\u2019s matrix tree theorem method to produce explicit formulas for the complexity of these graphs, using linear algebra, matrix analysis techniques, and employing knowledge of Chebyshev polynomials. Finally, we gave some numerical results for the number of spanning trees of the studied graphs.<\/jats:p>","DOI":"10.3390\/sym10120689","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T06:02:09Z","timestamp":1543816929000},"page":"689","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["The Complexity of Some Classes of Pyramid Graphs Created from a Gear Graph"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9620-7692","authenticated-orcid":false,"given":"Jia-Bao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3809-2521","authenticated-orcid":false,"given":"Salama Nagy","family":"Daoud","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia"},{"name":"Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,2]]},"reference":[{"key":"ref_1","unstructured":"Applegate, D.L., Bixby, R.E., Chv\u00e1tal, V., and Cook, W.J. 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