Monophonic numbers of the join and composition of connected graphs

In this paper, we describe the monophonic sets in the join and composition of two connected graphs. We also determine the monophonic numbers of the join of any two connected graphs and the composition G[Kn]G[Kn] of a connected graph G   and the complete graph KnKn. Lower and upper bounds are obtained for the monophonic number of the composition G[H]G[H], where G is connected and H is a connected non-complete graph.