Boolean Operations on Graphs
Boolean operations include the use of the logic operators AND, OR, and NOT applied to a number of arguments. There are Boolean functions on arguments. The state-of-the-art Boolean computation in Mathematica 8 makes it possible to apply arbitrary Boolean operations over graphs. This Demonstration shows the formula and result for each of the sixteen Boolean functions on two arguments operating on the complete graph on five vertices and the complete graph on three vertices. The counterparts of the operations AND, OR, and NOT for graphs are called union, intersection, and difference. The union of two graphs is obtained as the graph resulting from the union of their vertices and the union of their edges; the other operations are defined similarly.