Let  be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset  is a minimum neighborhood dominating set if  is a dominating set and if for every  holds. The minimum cardinality of the minimum neighborhood dominating set of a graph  is called as minimum neighborhood dominating number and it is denoted by  . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

In This paper, we introduce the associated graphs of commutative KU-algebra. Firstly, we define the KU-graph which is determined by all the elements of commutative KU-algebra as vertices. Secondly, the graph of equivalence classes of commutative KU-algebra is studied and several examples are presented. Also, by using the definition of graph folding, we prove that the graph of equivalence classes and the graph folding of commutative KU-algebra are the same, where the graph is complete bipartite graph.

Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be a complementary perfect corona dominating set (CPCD – set) if each vertex in  is either a pendent vertex or a support vertex and  has a perfect matching. The minimum cardinality of a complementary perfect corona dominating set is called the complementary perfect corona domination number and is denoted by . In this paper, our parameter hasbeen discussed for power graphs of path and cycle.

In the present paper, we have introduced some new definitions On D- compact topological group and D-L. compact topological group for the compactification in topological spaces and groups, we obtain some results related to D- compact topological group and D-L. compact topological group.

Assume that G is a finite group and X = tG where t is non-identity element with t3 = 1. The simple graph with node set being X such that a, b ∈ X, are adjacent if ab-1 is an involution element, is called the A4-graph, and designated by A4(G, X). In this article, the construction of A4(G, X) is analyzed for G is the twisted group of Lie type 3D4(3).

Recent years have seen an explosion in graph data from a variety of scientific, social and technological fields. From these fields, emotion recognition is an interesting research area because it finds many applications in real life such as in effective social robotics to increase the interactivity of the robot with human, driver safety during driving, pain monitoring during surgery etc. A novel facial emotion recognition based on graph mining has been proposed in this paper to make a paradigm shift in the way of representing the face region, where the face region is represented as a graph of nodes and edges and the gSpan frequent sub-graphs mining algorithm is used to find the frequent sub-structures in the graph database of each emotion. T

Background Psoriasis is one of the most prevalent chronic inflammatory skin conditions; its prevalence ranges from 1 to 3%. Tumor necrosis factor-alpha (TNF-α), a cytokine that enhances inflammation, is overexpressed in synovium and skin plaques in psoriasis. TNF-α plays a critical role in the pathogenesis of psoriasis. IL-10 is the most crucial cytokine for reducing excessive immune responses and decreasing pro-inflammatory reactions in all autoimmune disorders.   Objective To evaluate the effect of Apremilast on ILـ10, TNFـα, and BMI in obese psoriatic patients.   Methods Thirty patients included in this investigative study to measure the concentrations of TNFـα, ILـ10 and BMI, before and after receiving Apremilast. TNFـα and