{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T15:06:36Z","timestamp":1769180796257,"version":"3.49.0"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T00:00:00Z","timestamp":1641254400000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010814","name":"Anhui Provincial Department of Education","doi-asserted-by":"publisher","award":["KJ2020A0478"],"award-info":[{"award-number":["KJ2020A0478"]}],"id":[{"id":"10.13039\/501100010814","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    be the linear heptagonal networks with 2\n                    <jats:italic>n<\/jats:italic>\n                    heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    , we utilize the method of decompositions. Thus, the Laplacian spectrum of\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    is created by eigenvalues of a pair of matrices:\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    and\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>S<\/jats:italic>\n                    <\/jats:sub>\n                    of order numbers 5\n                    <jats:italic>n<\/jats:italic>\n                    + 1 and 4\n                    <jats:italic>n<\/jats:italic>\n                    + 1\n                    <jats:italic>n<\/jats:italic>\n                    !\/\n                    <jats:italic>r<\/jats:italic>\n                    ! (\n                    <jats:italic>n<\/jats:italic>\n                    \u2212\n                    <jats:italic>r<\/jats:italic>\n                    )!, respectively. On the basis of the roots and coefficients of their characteristic polynomials of\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>A<\/jats:italic>\n                    <\/jats:sub>\n                    and\n                    <jats:italic>L<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>S<\/jats:italic>\n                    <\/jats:sub>\n                    , we get not only the explicit forms of Kirchhoff index but also the corresponding total number of spanning trees of\n                    <jats:italic>H<\/jats:italic>\n                    <jats:sub>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sub>\n                    .\n                  <\/jats:p>","DOI":"10.1155\/2022\/5584167","type":"journal-article","created":{"date-parts":[[2022,1,4]],"date-time":"2022-01-04T19:50:06Z","timestamp":1641325806000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Laplacian Spectrum, Kirchhoff Index, and the Number of Spanning Trees of the Linear Heptagonal Networks"],"prefix":"10.1155","volume":"2022","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"}]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6941-3194","authenticated-orcid":false,"given":"Shaohui","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,1,4]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/qua.21537"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.02.019"},{"key":"e_1_2_8_3_2","first-page":"765","article-title":"On the kirchhoff index and the number of spanning trees of linear phenylenes","volume":"77","author":"Peng Y.","year":"2017","journal-title":"MATCH Commun. 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