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The D-neighborhood complex of a graph

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dc.contributor.authorPrevite, Corrine, author
dc.contributor.authorPeterson, Chris, advisor
dc.contributor.authorHulpke, Alexander, advisor
dc.contributor.authorBates, Dan, committee member
dc.contributor.authorGelfand, Martin, committee member
dc.date.accessioned2007-01-03T06:32:57Z
dc.date.available2007-01-03T06:32:57Z
dc.date.issued2014
dc.description.abstractThe Neighborhood complex of a graph, G, is an abstract simplicial complex formed by the subsets of the neighborhoods of all vertices in G. The construction of this simplicial complex can be generalized to use any subset of graph distances as a means to form the simplices in the associated simplicial complex. Consider a simple graph G with diameter d. Let D be a subset of {0,1,..., d}. For each vertex, u, the D-neighborhood is the simplex consisting of all vertices whose graph distance from u lies in D. The D-neighborhood complex of G, denoted DN(G,D), is the simplicial complex generated by the D-neighborhoods of vertices in G. We relate properties of the graph G with the homology of the chain complex associated to DN(G,D).
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierPrevite_colostate_0053A_12442.pdf
dc.identifier.urihttp://hdl.handle.net/10217/83806
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectcombinatorics
dc.subjectgraph theory
dc.subjecthomology
dc.subjectsimplicial complex
dc.subjecttopology
dc.titleThe D-neighborhood complex of a graph
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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