{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:12:39Z","timestamp":1760238759380,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T00:00:00Z","timestamp":1598313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Graovac\u2013Pisanski (GP) index of a graph is a modified version of the Wiener index based on the distance between each vertex x and its image \u03b1(x), where \u03b1 is an automorphism of graph. The aim of this paper is to compute the automorphism group of some classes of cubic polyhedral graphs and then we determine their Wiener index. In addition, we investigate the GP-index of these classes of graphs.<\/jats:p>","DOI":"10.3390\/sym12091411","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T09:24:56Z","timestamp":1598347496000},"page":"1411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analysis of the Graovac\u2013Pisanski Index of Some Polyhedral Graphs Based on Their Symmetry Group"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5623-9932","authenticated-orcid":false,"given":"Modjtaba","family":"Ghorbani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-136, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4638-6565","authenticated-orcid":false,"given":"Mardjan","family":"Hakimi-Nezhaad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-136, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8454-5857","authenticated-orcid":false,"given":"Matthias","family":"Dehmer","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Swiss Distance University of Applied Sciences, 3900 Brig, Switzerland"},{"name":"Department of Biomedical Computer Science and Mechatronics, UMIT, A-6060 Hall in Tyrol, Austria"},{"name":"College of Artficial Intelligence, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueliang","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Combinatorics, Nankai University, Tianjin 300071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1021\/ja01193a005","article-title":"Structural Determination of Paraffin Boiling Points","volume":"69","author":"Wiener","year":"1947","journal-title":"J. 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