{"title":"最小化具有固定大小和直径的二方图中的第二个萨格勒布偏心指数","authors":"Fazal Hayat, Shou-Jun Xu, Xuli Qi","doi":"10.1007/s12190-024-02163-8","DOIUrl":null,"url":null,"abstract":"<p>For a given graph <i>G</i>, the second Zagreb eccentricity index <span>\\(\\xi _2 (G)\\)</span> is defined as the product of the eccentricities of two adjacent vertex pairs in <i>G</i>. This paper mainly studies the problem of determining the graphs that minimize the second Zagreb eccentricity index among <i>n</i>-vertex bipartite graphs with a fixed number of edges and diameter. To be specific, we determine the sharp lower bound on the second Zagreb eccentricity index over the bipartite graphs of order <i>n</i> in terms of fixed edges and diameter. The extremal graphs attaining these lower bounds are fully characterized.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimizing the second Zagreb eccentricity index in bipartite graphs with a fixed size and diameter\",\"authors\":\"Fazal Hayat, Shou-Jun Xu, Xuli Qi\",\"doi\":\"10.1007/s12190-024-02163-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For a given graph <i>G</i>, the second Zagreb eccentricity index <span>\\\\(\\\\xi _2 (G)\\\\)</span> is defined as the product of the eccentricities of two adjacent vertex pairs in <i>G</i>. This paper mainly studies the problem of determining the graphs that minimize the second Zagreb eccentricity index among <i>n</i>-vertex bipartite graphs with a fixed number of edges and diameter. To be specific, we determine the sharp lower bound on the second Zagreb eccentricity index over the bipartite graphs of order <i>n</i> in terms of fixed edges and diameter. The extremal graphs attaining these lower bounds are fully characterized.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12190-024-02163-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12190-024-02163-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
对于给定的图 G，第二萨格勒布偏心指数（\xi _2 (G)\）被定义为 G 中两个相邻顶点对的偏心率的乘积。本文主要研究在具有固定边数和直径的 n 个顶点双artite图中确定最小化第二萨格勒布偏心指数的图的问题。具体地说，我们确定了在固定边数和直径的 n 阶双方形中第二萨格勒布偏心指数的尖锐下限。达到这些下界的极值图被完全表征出来。
Minimizing the second Zagreb eccentricity index in bipartite graphs with a fixed size and diameter
For a given graph G, the second Zagreb eccentricity index \(\xi _2 (G)\) is defined as the product of the eccentricities of two adjacent vertex pairs in G. This paper mainly studies the problem of determining the graphs that minimize the second Zagreb eccentricity index among n-vertex bipartite graphs with a fixed number of edges and diameter. To be specific, we determine the sharp lower bound on the second Zagreb eccentricity index over the bipartite graphs of order n in terms of fixed edges and diameter. The extremal graphs attaining these lower bounds are fully characterized.
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