ABSTRACT
This chapter is concerned with the independence number for the four standard products. The question is simple for the lexicographic product, and Exercise 27.1 gives a complete answer. The central concept of the first section, the Shannon capacity, involves the strong product, and in this case the determination of the independence number is extremely difficult. Section 27.2 studies the independence number of direct products, with a special emphasis on vertex-transitive graphs. We also treat the ultimate direct independence ratio, a concept parallel to the Shannon capacity. The final section investigates the independence number for the Cartesian product and introduces the ultimate Cartesian independence ratio.
