The D-neighborhood complex of a graph

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).

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2014

Authors dc:creator

• Previte, Corrine, author
• Peterson, Chris, advisor
• Hulpke, Alexander, advisor
• Bates, Dan, committee member
• Gelfand, Martin, committee member

• combinatorics
• graph theory
• homology
• simplicial complex
• topology

Statement 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.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.018305

OAI identifier oai:identifier

oai:mountainscholar.org:10217/83806