{"id":{"repo_id":"colostate","oai_identifier":"oai:mountainscholar.org:10217/83806"},"canonical_url":"https://search.dev.ndltd.org/etd/colostate/oai:mountainscholar.org:10217/83806","repository":{"repo_id":"colostate","name":"Colorado State University","base_url":"https://api.mountainscholar.org/server/oai/request"},"display":{"title":"The D-neighborhood complex of a graph","abstract":"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).","abstract_html":"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).","abstract_has_math":false,"creators":["Previte, Corrine, author","Peterson, Chris, advisor","Hulpke, Alexander, advisor","Bates, Dan, committee member","Gelfand, Martin, committee member"],"institution":"Colorado State University. Libraries","degree_name":"Doctor of Philosophy (Ph.D.)","degree_level":"Doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-27T19:12:54Z","subjects":["combinatorics","graph theory","homology","simplicial complex","topology"],"languages":["eng","English"],"rights":["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."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.25675/3.018305"],"render_values":[{"text":"https://doi.org/10.25675/3.018305","href":"https://doi.org/10.25675/3.018305","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10217/83806","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Previte, Corrine, author","Peterson, Chris, advisor","Hulpke, Alexander, advisor","Bates, Dan, committee member","Gelfand, Martin, committee member"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2007-01-03T06:32:57Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2007-01-03T06:32:57Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher","label":"Institution","values":["Colorado State University. Libraries"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (Ph.D.)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Colorado State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["combinatorics","graph theory","homology","simplicial complex","topology"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["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."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["Previte_colostate_0053A_12442.pdf"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10217/83806","https://doi.org/10.25675/3.018305"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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)."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["born digital","doctoral dissertations"]},{"key":"dc:title","label":"Title","values":["The D-neighborhood complex of a graph"]}]}],"canonical_facts":{"dc:creator":["Previte, Corrine, author","Peterson, Chris, advisor","Hulpke, Alexander, advisor","Bates, Dan, committee member","Gelfand, Martin, committee member"],"dc:date.accessioned":["2007-01-03T06:32:57Z"],"dc:date.available":["2007-01-03T06:32:57Z"],"dc:date.issued":["2014"],"dc:description.abstract":["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)."],"dc:format.medium":["born digital","doctoral dissertations"],"dc:identifier":["Previte_colostate_0053A_12442.pdf"],"dc:identifier.uri":["http://hdl.handle.net/10217/83806","https://doi.org/10.25675/3.018305"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["Colorado State University. Libraries"],"dc:rights":["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."],"dc:subject":["combinatorics","graph theory","homology","simplicial complex","topology"],"dc:title":["The D-neighborhood complex of a graph"],"dc:type":["Text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Doctoral"],"thesis:degree_name":["Doctor of Philosophy (Ph.D.)"],"thesis:institution_name":["Colorado State University"]},"updated_at":"2026-07-27T19:12:54Z"}