{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:38:22Z","timestamp":1760240302298,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T00:00:00Z","timestamp":1556755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571135"],"award-info":[{"award-number":["11571135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Humanities and Social Sciences of Ministry of Education Planning Fund","award":["16Y JA630032"],"award-info":[{"award-number":["16Y JA630032"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Resistance distance is a concept developed from electronic networks. The calculation of resistance distance in various circuits has attracted the attention of many engineers. This report considers the resistance-based graph invariant, the Resistance\u2013Harary index, which represents the sum of the reciprocal resistances of any vertex pair in the figure G, denoted by     R H ( G )    . Vertex bipartiteness in a graph G is the minimum number of vertices removed that makes the graph G become a bipartite graph. In this study, we give the upper bound and lower bound of the     R H     index, and describe the corresponding extremal graphs in the bipartite graph of a given order. We also describe the graphs with maximum     R H     index in terms of graph parameters such as vertex bipartiteness, cut edges, and matching numbers.<\/jats:p>","DOI":"10.3390\/sym11050615","type":"journal-article","created":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T03:15:22Z","timestamp":1556766922000},"page":"615","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extremal Bipartite Graphs with Given Parameters on the Resistance\u2013Harary Index"],"prefix":"10.3390","volume":"11","author":[{"given":"Hongzhuan","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China"}]},{"given":"Piaoyang","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Business, Huaiyin Institute of Technology, Huaian 223003, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,2]]},"reference":[{"key":"ref_1","unstructured":"Todeschini, R., and Consoni, V. 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