# Flanking numbers and its application to arankings of cyclic graphs

 dc.contributor.advisor Narayan, Darren dc.contributor.author Short, M. Daniel dc.date.accessioned 2011-05-25T14:03:47Z dc.date.available 2011-05-25T14:03:47Z dc.date.issued 2011-05-13 dc.identifier.uri http://hdl.handle.net/1850/13678 dc.description.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. en_US dc.language.iso en_US en_US dc.relation RIT Scholars content from RIT Digital Media Library has moved from http://ritdml.rit.edu/handle/1850/13678 to RIT Scholar Works http://scholarworks.rit.edu/theses/4996, please update your feeds & links! dc.subject Arank number en_US dc.subject Flanking number en_US dc.subject Graph theory en_US dc.subject Minimal ranking en_US dc.subject Ranking en_US dc.subject.lcc QA166 .S467 2011 dc.subject.lcsh Graph theory en_US dc.title Flanking numbers and its application to arankings of cyclic graphs en_US dc.type Thesis en_US dc.description.college College of Science en_US dc.description.department Department of Mathematics and Statistics en_US

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