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Doctoral Dissertation Announcement
Candidate: Futaba Okamoto
Degree of:
Doctor of Philosophy
Department: Mathematics
Title: Measures of Traversability in Graphs
Committee:
Dr. Ping Zhang, Chair
Dr. Gary Chartrand
Dr. Allen J. Schwenk
Dr. Arthur T. White
Dr. Garry L. Johns
Date: Thursday, April 19, 2007 3:00 p.m. – 5:00 p.m.
6625 Everett Tower
Abstract:
A graph G is Hamiltonian if G contains a spanning cycle; while a graph H is traceable if H contains a spanning path. Therefore, the vertices of G can be ordered to form a cyclic sequence so that every two consecutive vertices in the sequence are adjacent in G. Similarly, the vertices of H can be ordered to form a linear sequence so that every two consecutive vertices in the sequence are adjacent in H. Whether a connected graph G is Hamiltonian or not, the vertices of G can be ordered into a cyclic sequence such that the sum of the distances between every pair of consecutive vertices is minimum. Also, whether a connected graph H is traceable or not, the vertices of H can be ordered into a linear sequence such that the sum of the distances between every pair of consecutive vertices is minimum. The resulting sums provide two measures of traversability in graphs. These measures as well as other related measures are studied for our purpose of providing insight into the structure of graphs.