Abstract

Given a graph G with a ranking function, f: V(G) --> {1,2,...,k}, the ranking is minimal if only if G does not contain a drop vertex. The arank number of a graph, [psi]r(G), is the maximum k such that G has a minimal k-ranking. A new technique is established to better understand how to analyze arankings of various cyclic graphs, Cn. Then the technique, flanking number, is used to describe all arank properties of all cyclic graphs fully by proving the following proposition: [psi]r(C_n) = [floor]{log₂(n+1)[floor] + [floor]log₂(n+2/3)[floor] + 1 for all n > 6.

Library of Congress Subject Headings

Graph theory

Publication Date

5-13-2011

Document Type

Thesis

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Narayan, Darren

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA166 .S467 2011

Campus

RIT – Main Campus

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