In a graph G = (V,E), a subset $S⊂V$ is said to be an open packing set if no two vertices of S have a common neighbour in G. The maximum cardinality of an open packing set is called the open packing number and is denoted by $ρ^{o}$. This paper further studies on this parameter by obtaining some new bounds.

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...

By increasing house demand for living, the urban development planning has turned to towers, which provides a platform for the growth of the city, regardless of the traditional Iranian's architecture. Among the vital elements in traditional architecture, there are a variety of open and semi-open spaces such as the central courtyard, pool, veranda, balcony, etc that have been provided the needs f...

State of the art set expansion algorithms produce varying quality expansions for different entity types. Even for the highest quality expansions, errors still occur and manual refinements are necessary for most practical uses. In this paper, we propose algorithms to aide this refinement process, greatly reducing the amount of manual labor required. The methods rely on the fact that most expansi...

D. Molodtsov (1999) [1] introduced the concept of a soft set as a new approach for modeling uncertainties. Xiao et al. [7] and Pei and Miao [8] discussed the relationship between soft sets and information systems. They showed that soft sets are a class of special information systems. So it’s important to study the structures of soft sets for information systems. Shabir and Naz(2011) [20], studi...

formalized in terms of a hypergraph G = (V,E) whose edges arrive one-by-one and the goal is to construct an edge cover F ⊆ E with the objective of minimizing the cardinality (or cost in the weighted case) of F . We further consider a parameterized relaxation of this problem, where given some 0 ≤ < 1, the goal is to construct an edge (1− )-cover, namely, a subset of edges incident to all but an ...

In this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.