{"title":"相对于莫斯塔尔指数，具有两个全六角形的极值卡塔缩合苯并呋喃","authors":"","doi":"10.1080/10406638.2023.2266182","DOIUrl":null,"url":null,"abstract":"<div><div>The Mostar index <span><math><mrow><mi>M</mi><mi>o</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span> is the sum of absolute values of the differences between <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>u</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> and <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>v</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> over all edges <span><math><mrow><mi>e</mi><mo>=</mo><mi>u</mi><mi>v</mi></mrow></math></span> of <em>G</em>, where <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>u</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> and <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>v</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> are the number of vertices of <em>G</em> lying closer to vertex <em>u</em> than to vertex <em>v</em> and the number of vertices of <em>G</em> lying closer to vertex <em>v</em> than to vertex <em>u</em>, respectively. In this article, for given cata-condensed hexagonal systems with <em>p</em> hexagons, which have exactly two full-hexagons, we determine the extremal hexagonal system with the greatest Mostar index, and the corresponding formula of Mostar index is given.</div></div>","PeriodicalId":20303,"journal":{"name":"Polycyclic Aromatic Compounds","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Extremal Cata-Condensed Benzenoids with Two Full-Hexagons with Respect to the Mostar indices\",\"authors\":\"\",\"doi\":\"10.1080/10406638.2023.2266182\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Mostar index <span><math><mrow><mi>M</mi><mi>o</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span> is the sum of absolute values of the differences between <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>u</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> and <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>v</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> over all edges <span><math><mrow><mi>e</mi><mo>=</mo><mi>u</mi><mi>v</mi></mrow></math></span> of <em>G</em>, where <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>u</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> and <span><math><mrow><mrow><msub><mrow><mi>n</mi></mrow><mi>v</mi></msub></mrow><mo>(</mo><mi>e</mi><mo>)</mo></mrow></math></span> are the number of vertices of <em>G</em> lying closer to vertex <em>u</em> than to vertex <em>v</em> and the number of vertices of <em>G</em> lying closer to vertex <em>v</em> than to vertex <em>u</em>, respectively. In this article, for given cata-condensed hexagonal systems with <em>p</em> hexagons, which have exactly two full-hexagons, we determine the extremal hexagonal system with the greatest Mostar index, and the corresponding formula of Mostar index is given.</div></div>\",\"PeriodicalId\":20303,\"journal\":{\"name\":\"Polycyclic Aromatic Compounds\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Polycyclic Aromatic Compounds\",\"FirstCategoryId\":\"92\",\"ListUrlMain\":\"https://www.sciencedirect.com/org/science/article/pii/S1040663823020559\",\"RegionNum\":3,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, ORGANIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Polycyclic Aromatic Compounds","FirstCategoryId":"92","ListUrlMain":"https://www.sciencedirect.com/org/science/article/pii/S1040663823020559","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, ORGANIC","Score":null,"Total":0}
引用次数: 0
摘要
莫斯塔尔指数 Mo(G)是 G 的所有边 e=uv 上 nu(e)和 nv(e)之差的绝对值之和，其中 nu(e)和 nv(e)分别是 G 中靠近顶点 u 而不是顶点 v 的顶点数，以及 G 中靠近顶点 v 而不是顶点 u 的顶点数。本文针对具有 p 个六边形且恰好有两个全六边形的卡塔缩合六边形系统，确定了莫斯塔尔指数最大的极值六边形系统，并给出了相应的莫斯塔尔指数公式。
Extremal Cata-Condensed Benzenoids with Two Full-Hexagons with Respect to the Mostar indices
The Mostar index is the sum of absolute values of the differences between and over all edges of G, where and are the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, respectively. In this article, for given cata-condensed hexagonal systems with p hexagons, which have exactly two full-hexagons, we determine the extremal hexagonal system with the greatest Mostar index, and the corresponding formula of Mostar index is given.
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The purpose of Polycyclic Aromatic Compounds is to provide an international and interdisciplinary forum for all aspects of research related to polycyclic aromatic compounds (PAC). Topics range from fundamental research in chemistry (including synthetic and theoretical chemistry) and physics (including astrophysics), as well as thermodynamics, spectroscopy, analytical methods, and biology to applied studies in environmental science, biochemistry, toxicology, and industry. Polycyclic Aromatic Compounds has an outstanding Editorial Board and offers a rapid and efficient peer review process, as well as a flexible open access policy.
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