{"title":"关于闭影图的特征值","authors":"F. J. Campena, Melody Mae C. Lunar, Inseok Sung","doi":"10.1080/09720529.2022.2060609","DOIUrl":null,"url":null,"abstract":"Abstract The energy and d-energy of a graph is the sum of the absolute values of the graphs’ adjacency and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study we determine the eigenvalues and d-eigenvalues of a closed shadow graph. Thus, determining also the energy and distance energy of a closed shadow graph. As a consequence, the closed shadow graph of G is integral whenever G is integral, that is the eigenvalues of the adjacency matrix of the graph are all integers.","PeriodicalId":46563,"journal":{"name":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2022-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the eigenvalues of closed shadow graphs\",\"authors\":\"F. J. Campena, Melody Mae C. Lunar, Inseok Sung\",\"doi\":\"10.1080/09720529.2022.2060609\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The energy and d-energy of a graph is the sum of the absolute values of the graphs’ adjacency and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study we determine the eigenvalues and d-eigenvalues of a closed shadow graph. Thus, determining also the energy and distance energy of a closed shadow graph. As a consequence, the closed shadow graph of G is integral whenever G is integral, that is the eigenvalues of the adjacency matrix of the graph are all integers.\",\"PeriodicalId\":46563,\"journal\":{\"name\":\"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-08-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/09720529.2022.2060609\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/09720529.2022.2060609","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Abstract The energy and d-energy of a graph is the sum of the absolute values of the graphs’ adjacency and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study we determine the eigenvalues and d-eigenvalues of a closed shadow graph. Thus, determining also the energy and distance energy of a closed shadow graph. As a consequence, the closed shadow graph of G is integral whenever G is integral, that is the eigenvalues of the adjacency matrix of the graph are all integers.
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