{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:19:20Z","timestamp":1760239160229,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T00:00:00Z","timestamp":1600992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011891","name":"Universiti Malaysia terengganu","doi-asserted-by":"publisher","award":["55192\/6"],"award-info":[{"award-number":["55192\/6"]}],"id":[{"id":"10.13039\/501100011891","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randi\u0107 index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond connectivity and Randi\u0107 indices, denoted as ABC\u2212R index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of ABC\u2212R for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for ABC\u2212R index of such trees with given number of pendant vertices. The role of symmetry has great importance in different areas of graph theory especially in chemical graph theory.<\/jats:p>","DOI":"10.3390\/sym12101591","type":"journal-article","created":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T01:39:33Z","timestamp":1600997973000},"page":"1591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randi\u0107 Index"],"prefix":"10.3390","volume":"12","author":[{"given":"Wan Nor Nabila Nadia Wan","family":"Zuki","sequence":"first","affiliation":[{"name":"Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5795-3580","authenticated-orcid":false,"given":"Zhibin","family":"Du","sequence":"additional","affiliation":[{"name":"School of Software, South China Normal University, Foshan 528225, China"},{"name":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China"}]},{"given":"Muhammad","family":"Kamran Jamil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 46000, Pakistan"}]},{"given":"Roslan","family":"Hasni","sequence":"additional","affiliation":[{"name":"Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,25]]},"reference":[{"key":"ref_1","unstructured":"West, D.B. 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