{"title":"光谱半径相等的无限树族","authors":"Francesco Belardo, Maurizio Brunetti","doi":"10.1016/j.exco.2024.100138","DOIUrl":null,"url":null,"abstract":"<div><p>In this note we show that for each positive integer <span><math><mrow><mi>a</mi><mo>⩾</mo><mn>2</mn></mrow></math></span> there exist infinitely many trees whose spectral radius is equal to <span><math><msqrt><mrow><mn>2</mn><mi>a</mi></mrow></msqrt></math></span>. Such trees are obtained by replacing the central edge of the double star <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mi>a</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> with suitable bidegreed caterpillars.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100138"},"PeriodicalIF":0.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X24000041/pdfft?md5=163e05dcfa0673ec0b2a9629bf2ab099&pid=1-s2.0-S2666657X24000041-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Infinite families of trees with equal spectral radius\",\"authors\":\"Francesco Belardo, Maurizio Brunetti\",\"doi\":\"10.1016/j.exco.2024.100138\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this note we show that for each positive integer <span><math><mrow><mi>a</mi><mo>⩾</mo><mn>2</mn></mrow></math></span> there exist infinitely many trees whose spectral radius is equal to <span><math><msqrt><mrow><mn>2</mn><mi>a</mi></mrow></msqrt></math></span>. Such trees are obtained by replacing the central edge of the double star <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mi>a</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> with suitable bidegreed caterpillars.</p></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"5 \",\"pages\":\"Article 100138\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2666657X24000041/pdfft?md5=163e05dcfa0673ec0b2a9629bf2ab099&pid=1-s2.0-S2666657X24000041-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X24000041\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X24000041","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Infinite families of trees with equal spectral radius
In this note we show that for each positive integer there exist infinitely many trees whose spectral radius is equal to . Such trees are obtained by replacing the central edge of the double star with suitable bidegreed caterpillars.
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