Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2017
Committee Chair or Co-Chairs
Robert A. Beeler, Teresa Haynes
Committee Members
Robert Gardner, Rodney Keaton
Abstract
For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertices that are adjacent to v and places one pebble on v. A vertex x is reachable under a pebbling distribution f if there exists some sequence of rubbling and pebbling moves that places a pebble on x. A pebbling distribution where every vertex is reachable is called a rubbling configuration. The t-restricted optimal rubbling number of G is the minimum number of pebbles required for a rubbling configuration where no vertex is initially assigned more than t pebbles. Here we present results on the 1-restricted optimal rubbling number and the 2- restricted optimal rubbling number.
Document Type
Dissertation - unrestricted
Recommended Citation
Murphy, Kyle, "On t-Restricted Optimal Rubbling of Graphs" (2017). Electronic Theses and Dissertations. Paper 3251. https://dc.etsu.edu/etd/3251
Copyright
Copyright by the authors.