On generalized composed properties of generalized product graphs

<p>A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class all finite simple graphs. A set <em>S</em> vertices graph <em>G</em> said ℘-set if <em>G</em>[<em>S</em>]∈ ℘. The maximum and minimum cardinalities are denoted by <em>M</em><sub>℘</sub>(<em>G</em>) <em>m</em><sub>℘</sub>(<em>G</em>), respectively. If such that its cardinality equals or we say an <em>M</em><sub>℘</sub>-set <em>m</em><sub>℘</sub>-set <em>G</em>, In this paper, not only define six types using concepts product generalized product, but also obtain <em>M</em><sub>℘</sub> <em>m</em><sub>℘</sub> graphs in each type characterize <em>M</em><sub>℘</sub>-set.</p>