On strongly *-graphs and strongly multiplicative graphs

Abstract

This paper studies strongly *-graphs as a variation of strongly multiplicative graphs. We show that every strongly multiplicative graph induces a strongly *-graph. We establish a relationship between the upper bounds on the number of edges of strongly *-graphs λ* (n) and strongly multiplicative graphs, and identify a condition under which the upper bound for strongly ∗-graphs exceeds that of strongly multiplicative graphs, we show that this condition holds for infinitely many values of n. We derive explicit formulas for λ* (n). Finally, we prove the independence of several necessary conditions for graphs that do not admit strongly *-labeling.