Theses and Dissertations - UTB/UTPA
Date of Award
8-2009
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
First Advisor
Dr. Aruanava Mukherjea
Second Advisor
Dr. Michael Persans
Third Advisor
Dr. Ramendra Bose
Abstract
The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This thesis is concerned with writing a DNA algorithm which can be followed in the laboratory to produce an explicit solution of a given Road-Coloring problem. This kind of DNA approach was first introduced by Adleman to find an effective method of finding the solution of a given Hamiltonian Path Problem. The Road-Coloring Problem, though introduced over 30 years ago in 1977 by Adler, Goodwyn, and Weiss was only recently solved by Trahtman. But his solution does not give explicitly the synchronizing instruction.
Granting Institution
University of Texas-Pan American
Comments
Copyright 2009 Arindam Roy. All Rights Reserved.
https://www.proquest.com/dissertations-theses/dna-approach-road-coloring-problem/docview/305181068/se-2