The modular product and existential closure

摘要

In this article we study the modular product graph operation, denoted by <>, with particular emphasis on when the operation preserves the property of a graph being 3-existentially closed. We characterise when GOH is 3- e.c. provided that H is 3-e.c., and we establish two new infinite classes of 3-e.c. graphs of the form GOH, for which G need not be 3-e.c. itself.