On Minimal Topological Totally Closed Graphs

A dominating function (DF)of a graph G =(V,E )is a function f :V →[0 ,1 ]such that for all v in V, sum of the function values over the closed neighbourhood of v is at least one.The dominating function f is called a minimal dominating function (MDF),if f doesn ’t remain a DF when the function value at some vertex is reduced.In this paper we study some topological properties of the set of all MDFs of certain classes of graphs.

2009

In this note, we study some other properties of functions with strongly semi-closed graphs by utilizing semi-open sets and the semi-closure operator.

2007

In 1997, Park et al. [5] offered a new notion called δ-semiopen sets which are stronger than semi-open sets but weaker than δ-open sets. It is the aim of this paper to introduce and study some properties of functions with strongly δ-semiclosed graphs by utilizing δ-semiopen sets and the δ-semi-closure operator.

2008

In this paper, we study some properties of functions with strongly α-closed graphs by utilizing α-open sets and the α-closure operator.

IJMER

Abstract: In this paper, we introduce new type of continuous functions called strongly wgrα-continuous and perfectly wgrα- continuous and study some of its properties. Also we introduce the concept of wgrα-compact spaces and wgrα-connected spaces and some their properties are analyzed

Southeast Asian Bulletin of Mathematics

A new class of functions called faintly g-continuous functions has been defined and studied in topological space. Also, the relationships between faintly g-continuous functions and graphs are investigated.

Journal of Physics: Conference Series

The purpose of this paper is to introduce and investigate a new types of mappings with Strongly Closed Graphs in Topological spaces namely strongly e-θ-(resp. δ-βθ)-Closed Graphs by using the concepts of e-θ-(resp. δ-βθ)-open sets and e-θ-(resp. δ-βθ)-closure operator which were introduced by Murad ÄOzkoc and GÄulhan Aslim [1] (resp. Alaa. M. F, and Xiao-Song Yang [2]), several characterizations and fundamental properties concerning of such these mappings have been studied. Furthermore, some characterizations of strongly e-θ-(δ-βθ)-Closed Graphs and nearly Φ-compact spaces have been obtained.

Demonstratio Mathematica, 1994

have studied the concept of α-strongly θcontinuous functions and (α, θ)-closed graph. The aim of this paper is to investigate several new characterizations and properties of α-strongly θcontinuous functions and (α, θ)-closed graph. Also, we define a new type of functions called αθ-open functions, which is stronger than quasi α-open and hence strongly α-open, and we obtain some characterizations and properties for it. It is shown that the graph of f, G ( f ) is (α, θ)-closed graph if and only if for each filter base Ψ in X θ-converging to some p in X such that f (Ψ) α-converges to some q in Y holds, f ( p) = q.

International Journal of Mathematics Trends and Technology, 2017

In 2008, Caldas M, Jafari S. and Noiri T. [7] introduced the concept of maximal -open sets, minimal -closed sets, -semi-maximal open and semi-minimal closed sets in general topological settings. In the present paper a new class of sets called minimal -open sets and maximal -closed sets in a topological space are introduced which are the -open sets and -closed sets respectively. The complement of minimal -open set is a maximal closed set. Some properties of -semi maximal closed sets, -semi minimal open sets are studied. Keywords-Minimal -open set, Maximal -closed set, -semi-minimal open set, -semi-maximal closed set.