We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p, q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p, q). On the other hand, we construct a consistent example of a Tychonov countably compact semigroup containing a copy of C(p, q). In this paper we study the structural prope...

In this paper, the concept of continuous multifunctions for digraphs is introduced. It turns out that a digraph multifunction is continuous if and only if it is strong. We introduce the notion of dismantlable digraphs and show that it does generalize the dismantlable graphs and posets. Generalizing various previous results, we show that any dismantlable digraph has the almost fixed point proper...

Many science phenomena are described as interacting particle systems (IPS). The mean field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution a PDE, Vlasov Equation (VE). Yet, many applications demand on networks/graphs. In this paper, we interested in sequence directed graphs, or digraphs for short. It interesting to know, how associated with influences macrosco...

Novel bicyclic iminosugar derivatives fused thiazolidin-4-one were conveniently synthesized by double Pummerer rearrangements, and their HIV reverse transcriptase (RT) inhibitory activities were preliminary examined. The notable anti-HIV-RT activity demonstrated that such bicyclic azasugars hold potential as a new kind of HIV-RT inhibitors.

the hosoya index and the merrifield-simmons index are two types of graph invariants used in mathematical chemistry. in this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. furthermore, we obtain exact formulas of hosoya and merrifield-simmons indices for the set of bicyclic graphs, caterpillars and dual star.

The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

The exponent of the strong product of a digraph of order m and a digraph of order n is shown to be bounded above by m+n− 2, with equality for Zm ⊠Zn. The exponent and diameter of the strong product of a graph and a digraph are also investigated.

A digraph D is said to be an m-coloured digraph, if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A set N ⊆ V (D) of vertices of D is said to be a kernel by monochromatic paths of the m-coloured digraph D, if it satisfies the two following properties: (1) N is independent by monochromatic paths; i.e., f...