In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.

  This research aims to identify the economic design techniques and materials that can be used in the implementation of cosmetic supplements to the spaces of the dwelling. The research relied on the descriptive and analytical approach by describing and analyzing models of design techniques and materials that can be used in the production of cosmetic supplements in the interior spaces of the dwelling.
The results of the research concluded that the beautification of the spaces of the dwelling is one of the necessary and important pieces to add aesthetic touches to the internal spaces, and that the use of economic design techniques and materials contributes to the implementation of many pieces of complementary beautification of the

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.

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.

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