图论中的黄金分割率：调查

arXiv - MATH - History and Overview Pub Date : 2024-07-09 DOI:arxiv-2407.15860

Saeid Alikhani, Nima Ghanbari

{"title":"图论中的黄金分割率：调查","authors":"Saeid Alikhani, Nima Ghanbari","doi":"arxiv-2407.15860","DOIUrl":null,"url":null,"abstract":"Much has been written about the golden ratio $\\phi=\\frac{1+\\sqrt{5}}{2}$ and\nthis strange number appears mysteriously in many mathematical calculations. In\nthis article, we review the appearance of this number in the graph theory. More\nprecisely, we review the relevance of this number in topics such as the number\nof spanning trees, topological indices, energy, chromatic roots, domination\nroots and the number of domatic partitions of graphs.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"61 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Golden ratio in graph theory: A survey\",\"authors\":\"Saeid Alikhani, Nima Ghanbari\",\"doi\":\"arxiv-2407.15860\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Much has been written about the golden ratio $\\\\phi=\\\\frac{1+\\\\sqrt{5}}{2}$ and\\nthis strange number appears mysteriously in many mathematical calculations. In\\nthis article, we review the appearance of this number in the graph theory. More\\nprecisely, we review the relevance of this number in topics such as the number\\nof spanning trees, topological indices, energy, chromatic roots, domination\\nroots and the number of domatic partitions of graphs.\",\"PeriodicalId\":501462,\"journal\":{\"name\":\"arXiv - MATH - History and Overview\",\"volume\":\"61 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - History and Overview\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.15860\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.15860","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

关于黄金分割率$\phi=\frac{1+\sqrt{5}}{2}$的文章已经很多了，这个奇怪的数字在许多数学计算中都神秘地出现过。在本文中，我们将回顾这个数字在图论中的出现。更确切地说，我们回顾了这个数在诸如生成树数、拓扑指数、能量、色根、支配根和图的支配分区数等主题中的相关性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Golden ratio in graph theory: A survey

Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More precisely, we review the relevance of this number in topics such as the number of spanning trees, topological indices, energy, chromatic roots, domination roots and the number of domatic partitions of graphs.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - History and Overview

自引率

0.00%

发文量