{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:59:11Z","timestamp":1760147951796,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T00:00:00Z","timestamp":1678752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Fujian Province","award":["2022J011149","JAT200599"],"award-info":[{"award-number":["2022J011149","JAT200599"]}]},{"name":"Youth and Middle-aged Project of Fujian Province Education Department","award":["2022J011149","JAT200599"],"award-info":[{"award-number":["2022J011149","JAT200599"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Several topological indices are known to have widespread implications in a variety of research areas. Over the years, the Kirchhoff index has turned out to be an extremely significant and efficient index. In this paper, we propose the exact formulas for the expected values of the random polyomino chain to construct the multiplicative degree-Kirchhoff index and the additive degree-Kirchhoff index. We also carefully examine the highest degree of the expected values for a random polyomino chain through the multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index.<\/jats:p>","DOI":"10.3390\/sym15030718","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T03:29:16Z","timestamp":1678764556000},"page":"718","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Kirchhoff Index and Additive Kirchhoff Index Based on Multiplicative Degree for a Random Polyomino Chain"],"prefix":"10.3390","volume":"15","author":[{"given":"Meilian","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Engineering, Longyan University, Longyan 364012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Asif","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Xiamen University, Xiamen 361005, China"},{"name":"Faculty of Sciences, The Superior University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9815-7158","authenticated-orcid":false,"given":"Haidar","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fizza","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College Women University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Parvez","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, College of Engineering, Qassim University, Unaizah 56215, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01164627","article-title":"Resistance distance","volume":"12","author":"Klein","year":"1993","journal-title":"J. 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