Topological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.

Rutting is one of the most complex and widespread types of distress. The rutting is frequently observed on Iraqi roads, especially at the checkpoints, forming a significant hazard on the asphalt layers. Factors such as heavy loads and high temperatures contribute to this distress. Adding fibers to a hot mix asphalt (HMA) effectively improves performance and extends the lifespan of the flexible pavement. This article used glass, steel, and basalt fibers. The wheel tracking test assessed the fibre-asphalt mixture for rutting resistance and compared it with the mix without adding fibers (control HMA). Meanwhile, the microscopic structure of fibres and asphalt mixture modified with fibers was examined using the Field Emission Scanning E

The exploitation of obsolete recyclable resources including paper waste has the advantages of saving resources and environment protection. This study has been conducted to study utilizing paper waste to adsorb phenol which is one of the harmful organic compound byproducts deposited in the environment. The influence of different agitation methods, pH of the solution (3-11), initial phenol concentration (30-120ppm), adsorbent dose (0.5-2.5 g) and contact time (30-150 min) were studied. The highest phenol removal efficiency obtained was 86% with an adsorption capacity of 5.1 mg /g at optimization conditions (pH of 9, initial phenol concentration of 30 mg/L, an adsorbent dose of 2 g and contact time of 120min and at room temperature).

Agricultural development occupies an important position in the economies of developing countries, and its role is greater for the Arab countries. The first task is to provide food security for all the population through sustainable development, which includes the investment of available natural resources and employment opportunities for the rural population, As well as the provision of raw materials for agricultural processing in order to increase agricultural exports to reduce the balance of payments deficit. Sustainable development is linked to increased production and improvement, as well as to food security. On the one hand, it has to cope with the increase in population and if it is possible to achieve a surplus allocated for export, a

David Hare (b.1947) is one of the most critically acclaimed, contemporary British dramatists. A playwright, director and filmmaker, he has written more than thirty plays for the stage and seven original screen plays for cinema and TV (Susan Emerling, p.1). He began his dramatic career in the late sixties. Along with such dramatists as Howard Brenton and Trevor Griffiths, he writes in the aftermath of the "Angry Young Men" tradition of John Osborne. It is a well-known fact that the element of anger continued in the drama of the 1960s and became even more radicalized after the social, cultural and political unrests of 1968 by the dramatists of the "second wave" to whom Hare belongs (John Russell Taylor, p.14). Setting his plays in a variet

Tobacco products of all kinds are harmful to public health, so legislation has paid great attention to regulating the process of tobacco production and distribution, whether at the level of national or international legislation, in a way that achieves legal protection for these products, so the establishment of civil liability for tobacco companies as a result of harm to the smoker The positive and the negative provoked a jurisprudential dispute due to the specificity of the work of these companies, and the jurisprudence differed in the legal nature of tobacco companies ’liability between contractual and tort liability in a way that enables the injured smoker to obtain his right to compensation.

• Commercial papers are one of the most important tools of the contemporary monetary market, and many of those who deal with them are ignorant of the Shariah rulings related to them, hence the urgent need to know the most prominent Sharia rulings related to commercial papers, including the discount. It is an agreement between the bank and its customer requesting the discount (the holder of the commercial paper) under which the bank is required By accelerating the value of the paper to the customer, in exchange for the latter’s obligation to transfer the ownership of the fixed right in the paper to the bank by endorsing it to him as a transfer of ownership.
• The noble Islamic Sharia does not prohibit dealing in commercial papers