{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:49Z","timestamp":1760146969201,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T00:00:00Z","timestamp":1734998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2024R231"],"award-info":[{"award-number":["PNURSP2024R231"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>An algebraic graph is defined in terms of graph theory as a graph with related algebraic structures or characteristics. If the vertex set of a graph G is a group, a ring, or a field, then G is called an algebraic structure graph. This work uses an algebraic structure graph based on the modular ring Zn, known as a hyper-chordal ring network. The lower and upper bounds of the local fractional metric dimension are computed for certain families of hyper-chordal ring networks. Utilizing the cardinalities of local fractional resolving sets, local fractional resolving (LFR)M-polynomials are computed for hyper-chordal ring networks. Further, new topological indices based on (LFR)M-polynomials are established for the proposed networks. The local fraction entropies are developed by modifying the first three kinds of Zagreb entropies, which are calculated for the chosen hyper-chordal ring networks. Furthermore, numerical and graphical comparisons are discussed to observe the order between newly computed topological indices.<\/jats:p>","DOI":"10.3390\/sym17010005","type":"journal-article","created":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T10:58:32Z","timestamp":1735037912000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Local Fractional Topological Indices and Entropies for Hyper-Chordal Ring Networks Using Local Fractional Metric Dimension"],"prefix":"10.3390","volume":"17","author":[{"given":"Shahzad","family":"Ali","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8616-8829","authenticated-orcid":false,"given":"Shahzaib","family":"Ashraf","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Khwaja Fareed University of Engineering and Information Technology, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5998-0053","authenticated-orcid":false,"given":"Shahbaz","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Kahn Campus, Rahim Yar Khan 64200, Pakistan"}]},{"given":"Abdullah","family":"Afzal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Rahim Yar Kahn Campus, Rahim Yar Khan 64200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7856-2861","authenticated-orcid":false,"given":"Amal S.","family":"Alali","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,24]]},"reference":[{"key":"ref_1","first-page":"128037","article-title":"Redefining fractal cubic networks and determining their metric dimension and fault-tolerant metric dimension","volume":"452","author":"Arulperumjothi","year":"2023","journal-title":"Appl. Math. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/s40314-023-02351-5","article-title":"Graphs whose mixed metric dimension is equal to their order","volume":"42","author":"Ghalavand","year":"2023","journal-title":"Comput. Appl. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.dam.2016.12.021","article-title":"On optimal approximability results for computing the strong metric dimension","volume":"221","author":"DasGupta","year":"2017","journal-title":"Discrete Appl. 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