## Finding Cycles In The Kth Power Diagraphs Over Integers Modulo A Prime And Over Gaussian Integers Modulo a Gaussian Prime (thesis)

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Tu, Wenda

##### Subject

Washington and Lee University -- Honors in Mathematics

Numbers, Prime

Number theory

Graph theory

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Thesis; [FULL-TEXT RESTRICTED TO WASHINGTON AND LEE UNIVERSITY LOGIN] Wenda Tu is a member of the Class of 2014 of Washington and Lee University. Given Zp where p is an integer prime, let's de ne G(k) p to be the digraph whose set of vertices is Zp such that there is a directed edge from a vertex a to a vertex b if ak b mod p. First, we nd our own way to decide if there is a cycle of length t in a given graph G(k) p in Zp. Later, we extend our work from Zp to Z[i]=hpi for p Gaussian primes. We found similar ways to determine the cycles in G(k) p in such Gaussian integer eld .