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 - Withheld

Copyright

Nicholas Carney

Available for download on Tuesday, July 11, 2023

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