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Independence Complexes of Certain Families of Graphs

The focus of this report will be on independence complexes constructed from independent sets of members of sequences graphs. For such independence complexes, we will study generating functions and closed formulae for the Euler characteristics and f-polynomials, as well as homology groups of different degrees. All of these can be computed by hand, although this quickly becomes tedious as well as really difficult to do, hence recursive methods will be used instead. the generating functions, bounded formulae and recursive equations will be compared to known number sequences, and where possible bijections to other problems will be establised. For the independence complexes of each graphs sequence, formulae will be given for where the homology groups are nonzero, as well as in some cases formulae for the exact dimensions of the homology groups for each complex.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-38265
Date January 2011
CreatorsFors, Rickard
PublisherKTH, Skolan för datavetenskap och kommunikation (CSC), KTH, Matematik (Inst.)
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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