An outer-connected dominating set for an arbitrary graph G is a set D̃ ⊆ V such that D̃ is a dominating set and the induced subgraph G[V \ D̃] be connected. In this paper, we focus on the outerconnected domination number of the product of graphs. We investigate the existence of outer-connected dominating set in lexicographic product and Corona of two arbitrary graphs, and we present upper bounds f...

We study the Riesz decomposition property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.

A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G. In this paper improved lower and upper bounds for ψk of the Cartesian and the direct product of paths are derived. It is shown that for ψ3 those bounds are tight. For the lexicographic produc...

The natural lexicographic semigroupoids associated with Cantor product spaces indexed by countable linear orders are classified. Applications are given to the classification of triangular operator algebras which are direct limits of upper-triangular matrix algebras. 0. Introduction Consider a Cantor space which is presented explicitly as an infinite product of finite topological spaces. The pro...

In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ◦H is non-trivial and complete, then G ◦H is edge-transitive if and only if H is the lexicogr...

A regular nonempty graph Γ is called edge regular, whenever there exists a nonegative integer λΓ, such that any two adjacent vertices of Γ have precisely λΓ common neighbours. An edge regular graph Γ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer μΓ, such that any two vertices at distance 2 have precisely μΓ common neighbours...