{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T22:00:10Z","timestamp":1757541610774,"version":"3.41.2"},"reference-count":27,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T00:00:00Z","timestamp":1552348800000},"content-version":"vor","delay-in-days":70,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601006"],"award-info":[{"award-number":["11601006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"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":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this work, using knowledge of difference equations, we drive the explicit formulas for the number of spanning trees in the sequence of some graphs generated by a triangle by electrically equivalent transformations and rules of weighted generating function. Finally, we compare the entropy of our graphs with other studied graphs with average degree being 4, 5, and 6.<\/jats:p>","DOI":"10.1155\/2019\/4271783","type":"journal-article","created":{"date-parts":[[2019,3,12]],"date-time":"2019-03-12T23:30:54Z","timestamp":1552433454000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Number of Spanning Trees in the Sequence of Some Graphs"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9620-7692","authenticated-orcid":false,"given":"Jia-Bao","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3809-2521","authenticated-orcid":false,"given":"S. N.","family":"Daoud","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,3,12]]},"reference":[{"key":"e_1_2_14_1_2","series-title":"Princeton Series in Applied Mathematics","volume-title":"The Traveling Salesman Problem: A Computational Study","author":"Applegate D. L.","year":"2006"},{"key":"e_1_2_14_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.06.017"},{"key":"e_1_2_14_3_2","first-page":"263","article-title":"A theorem for counting spanning trees in general chemical graphs and its particular application to toroidal fullerenes","volume":"77","author":"Kirby E. C.","year":"2004","journal-title":"Croatica Chemica Acta"},{"key":"e_1_2_14_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.20300"},{"key":"e_1_2_14_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.12.035"},{"key":"e_1_2_14_6_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/10\/6\/004"},{"key":"e_1_2_14_7_2","first-page":"264","article-title":"Asymptotic enumeration theorems for the number of spanning trees and Eulerian trail in circulant digraphs & graphs","volume":"43","author":"Zhang F.","year":"1999","journal-title":"Science in China Series A"},{"key":"e_1_2_14_8_2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/45\/2\/025102"},{"key":"e_1_2_14_9_2","doi-asserted-by":"crossref","unstructured":"AtajanT.andInabaH. Network reliability analysis by counting the number of spanning trees Proceedings of the IEEE International Symposium on Communications and Information Technologies ISCIT 2004 October 2004 Japan IEEE 601\u2013604 2-s2.0-21844463093.","DOI":"10.1109\/ISCIT.2004.1412916"},{"key":"e_1_2_14_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2015.07.001"},{"key":"e_1_2_14_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230210404"},{"key":"e_1_2_14_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00034-4"},{"key":"e_1_2_14_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/andp.18471481202"},{"key":"e_1_2_14_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90065-3"},{"volume-title":"Algebraic Graph Theory","year":"1993","author":"Biggs N. L.","key":"e_1_2_14_15_2"},{"key":"e_1_2_14_16_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2015-15217-y"},{"key":"e_1_2_14_17_2","first-page":"85","article-title":"Number of spanning trees in different product of complete and complete tripartite graphs","volume":"139","author":"Daoud S. N.","year":"2018","journal-title":"Ars Combinatoria"},{"key":"e_1_2_14_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.joems.2017.07.005"},{"key":"e_1_2_14_19_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym10120689"},{"key":"e_1_2_14_20_2","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2014-14146-7"},{"key":"e_1_2_14_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.08.028"},{"key":"e_1_2_14_22_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/10\/6\/004"},{"key":"e_1_2_14_23_2","doi-asserted-by":"publisher","DOI":"10.1017\/S096354830500684X"},{"key":"e_1_2_14_24_2","first-page":"65","article-title":"Counting spanning trees in prism and anti-prism graphs","volume":"6","author":"Sun W.","year":"2016","journal-title":"Journal of Applied Analysis and Computation"},{"key":"e_1_2_14_25_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2013\/09\/p09015"},{"key":"e_1_2_14_26_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.83.016116"},{"key":"e_1_2_14_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-006-9262-0"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/4271783.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/4271783.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/4271783","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T11:19:38Z","timestamp":1723029578000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/4271783"}},"subtitle":[],"editor":[{"given":"Diego R.","family":"Amancio","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/4271783"],"URL":"https:\/\/doi.org\/10.1155\/2019\/4271783","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2018-10-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-01-09","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-03-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"4271783"}}