{"title":"Groups and Expanders","authors":"A. Lubotzky, B. Weiss","doi":"10.1090/dimacs/010/08","DOIUrl":"https://doi.org/10.1090/dimacs/010/08","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116874743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ramanujan Graphs and Diagrams Function Field Approach","authors":"Moshe Morgenstern","doi":"10.1090/dimacs/010/09","DOIUrl":"https://doi.org/10.1090/dimacs/010/09","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129424380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spectral Geometry and the Cheeger Constant","authors":"R. Brooks","doi":"10.1090/dimacs/010/02","DOIUrl":"https://doi.org/10.1090/dimacs/010/02","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131018076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we extend some earlier computations 8]. In particular, the expanding behavior of Cayley graphs of PSL2(F107) is compared with that of the Cayley graphs for the group A10. These computations support the (up to now) unvoiced conjecture of Lubotzky that the symmetric groups and projective linear groups have asymptotically diierent average expanding behavior. We also give a thorough spectral analysis for a natural family of Cayley graphs which does not admit analysis by Selberg's theorem.
{"title":"Numerical Investigation of the Spectrum for Certain Families of Cayley Graphs","authors":"J. Lafferty, D. Rockmore","doi":"10.1090/dimacs/010/06","DOIUrl":"https://doi.org/10.1090/dimacs/010/06","url":null,"abstract":"In this paper we extend some earlier computations 8]. In particular, the expanding behavior of Cayley graphs of PSL2(F107) is compared with that of the Cayley graphs for the group A10. These computations support the (up to now) unvoiced conjecture of Lubotzky that the symmetric groups and projective linear groups have asymptotically diierent average expanding behavior. We also give a thorough spectral analysis for a natural family of Cayley graphs which does not admit analysis by Selberg's theorem.","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126683992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Uniform Sampling Modulo a Group of Symmetries Using Markov Chain Simulation","authors":"M. Jerrum","doi":"10.1090/dimacs/010/04","DOIUrl":"https://doi.org/10.1090/dimacs/010/04","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129922410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Laplacian of a Hypergraph","authors":"F. Graham","doi":"10.1090/dimacs/010/03","DOIUrl":"https://doi.org/10.1090/dimacs/010/03","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129114487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some Algebraic Constructions of Dense Graphs of Large Girth and of Large Size","authors":"F. Lazebnik, V. Ustimenko","doi":"10.1090/dimacs/010/07","DOIUrl":"https://doi.org/10.1090/dimacs/010/07","url":null,"abstract":"","PeriodicalId":343292,"journal":{"name":"Expanding Graphs","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115670389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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