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oai:mountainscholar.org:10217/838062025-12-30T03:12:45Zcom_10217_100532com_10217_100000com_10217_100468com_10217_100303col_10217_100538col_10217_100469

Previte, Corrine, author Peterson, Chris, advisor Hulpke, Alexander, advisor Bates, Dan, committee member Gelfand, Martin, committee member 2007-01-03T06:32:57Z 2007-01-03T06:32:57Z 2014 Previte_colostate_0053A_12442.pdf http://hdl.handle.net/10217/83806 https://doi.org/10.25675/3.018305 The 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). born digital doctoral dissertations English eng Colorado State University. Libraries 2000-2019 Copyright 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. combinatorics graph theory homology simplicial complex topology The D-neighborhood complex of a graph Text Doctor of Philosophy (Ph.D.) Doctoral Mathematics Colorado State University This 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). open.access