On generalized composed properties of generalized product graphs - Nopparat Pleanmani; Sayan Panma (Indonesian Combinatorial Society (InaCombS), 2022)
A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class of all finite simple graphs. A nonempty set S of vertices of a graph G is said to be a ℘-set of G if G[S]∈ ℘. The maximum and minimum cardinalities of a ℘-set of G are denoted by M℘(G) and m℘(G), respectively. If S is a ℘-set such that its cardinality equals M℘(G) or m℘(G), we say that S is an M℘-set or an m℘-set of G, respectively. In this paper, we not only define six types of property ℘ by the using concepts of graph product and generalized graph product, but we also obtain M℘ and m℘ of product graphs in each type and characterize its M℘-set.