On Strongly Multiplicative Graphs

Abstract

We give a characterization of strongly multiplicative graphs. First, we introduce some necessary conditions for a graph to be strongly multiplicative.Second, we discuss the independence of these necessary conditions. Third, we show that they are altogether not sufficient for a graph to be strongly multiplicative. Fourth, we add another necessary condition. Fifth, we prove that this necessary condition is stronger than the mentioned necessary conditions except one. Finally, we conjecture that the condition itself is stronger than all of them.