Electronic Theses and Dissertations

Award/Availability

Thesis (UNI Access Only)

Keywords

Directed graphs; Graph theory; Combinatorial geometry; Lights out (Game);

Abstract

We will figure out when graphs are solvable in the Lights Out game and what graphs can have any initial configurations which are solvable. We will observe wheel, cycle, path, Km,n and join graphs. We will apply the Rule 90 in cellular automaton to cycle graphs. The Rule 90 in cellular automaton behaves like pushing “on” vertices automatically. Since configurations on cycle graphs change with time (steps) by the cellular automaton’s rule, we will consider what kind of cycle graphs and initial states can be solvable after finitely many steps. Solvable here means all vertices become “off”.

Date of Award

2016

Degree Name

Master of Arts

Department

Department of Mathematics

First Advisor

Douglas J. Shaw, Chair

Date Original

2016

Object Description

1 PDF file (x, 53 pages)

Language

EN

File Format

application/pdf

Available for download on Tuesday, April 25, 2017

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