{"title":"关于Seidel和Seidel-Laplace矩阵的一个注记","authors":"Jalal Askari","doi":"10.5269/bspm.51593","DOIUrl":null,"url":null,"abstract":"In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the Seidel and Seidel Laplacian matrices\",\"authors\":\"Jalal Askari\",\"doi\":\"10.5269/bspm.51593\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.\",\"PeriodicalId\":44941,\"journal\":{\"name\":\"Boletim Sociedade Paranaense de Matematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boletim Sociedade Paranaense de Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5269/bspm.51593\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.51593","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A note on the Seidel and Seidel Laplacian matrices
In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.