{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:48:02Z","timestamp":1760147282983,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T00:00:00Z","timestamp":1674086400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61702291","23","22A790017","55"],"award-info":[{"award-number":["61702291","23","22A790017","55"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"2020 International Cultivation Project of Henan Advanced Talents","award":["61702291","23","22A790017","55"],"award-info":[{"award-number":["61702291","23","22A790017","55"]}]},{"name":"Key Scientific and Technological Project in Henan Province","award":["61702291","23","22A790017","55"],"award-info":[{"award-number":["61702291","23","22A790017","55"]}]},{"name":"Key Scientific Research Project of Colleges and Universities in Henan Province","award":["61702291","23","22A790017","55"],"award-info":[{"award-number":["61702291","23","22A790017","55"]}]},{"name":"2021-2022 Scientific Research Funds for Selected Outstanding Returnees of Study Abroad Chinese Scholars of Henan Province of China","award":["61702291","23","22A790017","55"],"award-info":[{"award-number":["61702291","23","22A790017","55"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetry widely exists in many complex and real-world networks, with flower networks and sunflower networks being two richly symmetric networks and having many practical applications due to their special structures. The number of subtrees (the subtree number index) is closely related to the reliable network design. Using a generating function, structural analysis techniques, and auxiliary structure introduction, this paper presents the subtree generating functions of flower networks Fln,m(n\u22653,m\u22652) and sunflower networks Sfn,m(n\u22653,m\u22652) and, thus, solves the computation of subtree number indices of Fln,m(n\u22653,m\u22652) and Sfn,m(n\u22653,m\u22652). The results provide a fundamental and efficient method for exploring novel features of symmetric complex cyclic networks from the structural subtree number index perspective. For instance, we conclude that under some parameter constraints, the flower networks are more reliable than sunflower networks.<\/jats:p>","DOI":"10.3390\/sym15020284","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T06:22:10Z","timestamp":1674109330000},"page":"284","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enumerating Subtrees of Flower and Sunflower Networks"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3969-9317","authenticated-orcid":false,"given":"Long","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, China"},{"name":"School of Software, Pingdingshan University, Pingdingshan 467000, China"},{"name":"Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China"}]},{"given":"Zongpu","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, China"}]},{"given":"Yu","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454003, China"},{"name":"School of Software, Pingdingshan University, Pingdingshan 467000, China"},{"name":"Henan International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China"}]},{"given":"Fengge","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Software, Pingdingshan University, Pingdingshan 467000, China"}]},{"given":"Hailian","family":"Lv","sequence":"additional","affiliation":[{"name":"School of Software, Pingdingshan University, Pingdingshan 467000, China"}]},{"given":"Weiting","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Software, Pingdingshan University, Pingdingshan 467000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1038\/nature21723","article-title":"Evolutionary dynamics on any population structure","volume":"544","author":"Allen","year":"2017","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1238411","DOI":"10.1126\/science.1238411","article-title":"Structural and functional brain networks: From connections to cognition","volume":"342","author":"Park","year":"2013","journal-title":"Science"},{"key":"ref_3","first-page":"1","article-title":"Social evolution in structured populations","volume":"5","author":"Hauert","year":"2014","journal-title":"Nat. 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