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Abstract

Critical to the understanding of a graph are its chromatic number and whether or not it is perfect. Here we prove when G (Zn), the zero-divisor graph of Zn, is perfect and show an alternative method to Duane for determining the chromatic number in those cases. We go on to determine the chromatic number for G(Zp[x]/< xn>) where p is prime and show that an isomorphism exists between this graph and G(Zpn).

Author Bio

Dan Endean is a junior at St. Olaf College majoring in mathematics and physics. He plans to study in Budapest, Hungary this coming spring and attend graduate school after graduation. Currently he is also working as a researcher for Professor Jason Engbrecht at St. Olaf College producing computer simulations of positron flight in a Penning trap. He also enjoys sailing, biking, waterskiing and woodworking.

Erin Manlove is a summa cum laude graduate of St. Olaf College with honors in mathematics and physics. While an undergraduate, she took part in summer physics research with Professor Brian Borovsky of St. Olaf College, and she participated in the University of Nebraska-Lincoln IMMERSE summer math program. She will attend mathematics graduate school at the University of Minnesota-Twin Cities. In her spare time, she enjoys playing viola and going running.

Kristin Henry graduated from St. Olaf College with a double major in mathematics and chemistry, and she will begin her professional studies in pharmacy at the University of Wisconsin - Madison in the fall of 2007. She loves doing creative things with her free time such as sewing, oil painting, and playing the violin.

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