The clique number of generalized Hamming graphs [Elektronische Ressource] / submitted by Elham Sharifiyazdi

The Clique Number of Generalized HammingGraphsDoctoral Thesis(Dissertation)to be awarded the degree ofDoctor rerum naturalium (Dr. rer. nat.)submitted byElham Sharifiyazdifrom Iranapproved by the Faculty of Mathematics/Computer Sciences and EngineeringClausthal University of TechnologyDate of oral examination5 October 2007Chairperson of the Board of ExaminersProf. Dr.-Ing. N. Mu¨llerChief ReviewerProf. Dr. W. KlotzReviewerProf. Dr. J. W. SanderAcknowledgementsFirst and foremost, I would like to thank my supervisor, Prof. Walter Klotz.The most influential and constructive ideas in this thesis came from him. Iam grateful to him for his enthusiastic supervision of all aspects from aca-demic advice to correcting the punctuation in my thesis. I also thank Prof.J. W. Sander, the second reader of this thesis, for his helpful comments.I would like to thank the faculty and the staff of the Institute of Mathe-matics at the Technical University of Clausthal.Last but not least, I would like to express my love and gratitude to myhusband, my son and my parents for their love and support. This thesis isdedicated to them.Contents1 Introduction 32 Identities for Binomial Coefficients 73 Hamming Graphs with Even Distance 194 Hamming Graphs with Odd Distance 335 Binary Hamming Graphs 696 Further Results 797 Conclusion 9512 CONTENTSChapter 1IntroductionLet A ,...,A be non-empty, finite sets (alphabets). The elements of the1 nCartesian productV =A ×...