{"title":"Kirchhoff index of the connections of two networks by an edge","authors":"Silvia Gago","doi":"10.1016/j.endm.2018.06.049","DOIUrl":null,"url":null,"abstract":"<div><p>In this work we compute the group inverse of the Laplacian of the connections of two networks by and edge in terms of the Laplacians of the original networks. Thus the effective resistances and Kirchhoff index of the new network can be derived from the Kirchhoff indexes of the original networks.</p></div>","PeriodicalId":35408,"journal":{"name":"Electronic Notes in Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.endm.2018.06.049","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Notes in Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1571065318301409","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
In this work we compute the group inverse of the Laplacian of the connections of two networks by and edge in terms of the Laplacians of the original networks. Thus the effective resistances and Kirchhoff index of the new network can be derived from the Kirchhoff indexes of the original networks.
期刊介绍:
Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.