## Electronic Theses and Dissertations

#### Title

Roman Domination Cover Rubbling

#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

8-2019

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