Flanking numbers and its application to arankings of cyclic graphs

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Title: Flanking numbers and its application to arankings of cyclic graphs
Author: Short, M. Daniel
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.
Record URI: http://hdl.handle.net/1850/13678
Date: 2011-05-13

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