DOI
https://doi.org/10.25772/9XSA-TJ11
Defense Date
2011
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Dewey Taylor
Abstract
An odd open dominating set of a graph is a subset of the graph’s vertices with the property that the open neighborhood of each vertex in the graph contains an odd number of vertices in the subset. An odd closed r-dominating set is a subset of the graph’s vertices with the property that the closed r-ball centered at each vertex in the graph contains an odd number of vertices in the subset. We first prove that the n-fold direct product of simple graphs has an odd open dominating set if and only if each factor has an odd open dominating set. Secondly, we prove that the n-fold strong product of simple graphs has an odd closed r-dominating set if and only if each factor has an odd closed r-dominating set.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
July 2011