Date of Award
We study the zero divisor graphs, determined by equivalence classes of zero divisors of a ring R. with exactly five vertices. In particular, we determine which graphs with exactly five vertices can be realized as the zero divisor graph of a ring. We provide rings for the graphs which are possible, and prove that the rest of graphs can not be realized via any commutative ring. There are thirty-four graphs in total which contain exactly five vertices.
Levidiotis, Florida Victoria, "Five Point Zero Divisor Graphs" (2010). Honors Theses. 2053.