Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
8-2019
Committee Chair or Co-Chairs
Rodney Keaton
Committee Members
Robert A. Beeler, Teresa Haynes
Abstract
In this thesis, we introduce Roman domination cover rubbling as an extension of domination cover rubbling. We define a parameter on a graph $G$ called the \textit{Roman domination cover rubbling number}, denoted $\rho_{R}(G)$, as the smallest number of pebbles, so that from any initial configuration of those pebbles on $G$, it is possible to obtain a configuration which is Roman dominating after some sequence of pebbling and rubbling moves. We begin by characterizing graphs $G$ having small $\rho_{R}(G)$ value. Among other things, we also obtain the Roman domination cover rubbling number for paths and give an upper bound for the Roman domination cover rubbling number of a tree.
Document Type
Thesis - unrestricted
Recommended Citation
Carney, Nicholas, "Roman Domination Cover Rubbling" (2019). Electronic Theses and Dissertations. Paper 3617. https://dc.etsu.edu/etd/3617
Copyright
Nicholas Carney