{"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}
引用次数: 0
Abstract
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.
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