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).
Jill Dietz, Department of Mathematics, St. Olaf Collegedietz@stolaf.edu
Endean, Daniel; Manlove, Erin; and Henry, Kristin
"Zero-Divisor Graphs of Zn and Polynomial Quotient Rings over Zn,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8
, Article 5.
Available at: http://scholar.rose-hulman.edu/rhumj/vol8/iss2/5