For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

The main objective of this paper is to designed algorithms and implemented in the construction of the main program designated for the determination the tenser product of representation for the special linear group.

In this paper, we show that for the alternating group An, the class C of n- cycle, CC covers An for n when n = 4k + 1 > 5 and odd. This class splits into two classes of An denoted by C and C/, CC= C/C/ was found.

The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .

This booklet contains the basic data and graphs forCOVID-19 in Iraq during the first three months of thepandemic ( 24 February to 19 May - 2020 ) , It isperformed to help researchers regarding this health problem (PDF) Information Booklet COVID-19 Graphs For Iraq First 3 Months. Available from: https://www.researchgate.net/publication/341655944_Information_Booklet_COVID-19_Graphs_For_Iraq_First_3_Months#fullTextFileContent [accessed Oct 26 2024].

The aim of this paper is to generate topological structure on the power set of vertices of digraphs using new definition which is Gm-closure operator on out-linked of digraphs. Properties of this topological structure are studied and several examples are given. Also we give some new generalizations of some definitions in digraphs to the some known definitions in topology which are Ropen subgraph, α-open subgraph, pre-open subgraph, and β-open subgraph. Furthermore, we define and study the accuracy of these new generalizations on subgraps and paths.

A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs.