Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

Since the COVID-19 pandemic alarm was made by the severe acute respiratory syndrome (SARS)-coronavirus (CoV) 2, several institutions and agencies have pursued to clarify the viral virulence and infectivity. The fast propagation of this virus leads to an unprecedented rise in the number of cases worldwide. COVID-19 virus is exceptionally contagious that spreads through droplets, respiratory secretions, and direct contact. The enveloped, single-stranded RNA virus has a specific envelop region called (S) region encoding (S protein) that specifically binds to the host cell receptor. Viral infection requires receptors' participation on the host cell membrane's surface, a  key- step for the viral invasion of susceptible cells.

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In this work,  the study of corona domination in graphs is carried over which was initially proposed by G. Mahadevan et al. Let be a simple graph. A dominating set S of a graph is said to be a corona-dominating set if every vertex in is either a pendant vertex or a support vertex. The minimum cardinality among all corona-dominating sets is called the corona-domination number and is denoted by (i.e) . In this work, the exact value of the corona domination number for some specific types of graphs are given. Also, some results on the corona domination number for some classes of graphs are obtained and the method used in this paper is a well-known number theory concept with some modification this method can also be applied to obt

In this paper We introduce some new types of almost bi-periodic points in topological bitransfprmation groups and thier effects on some types of minimaliy in topological dynamics

The purpose of this resesrh know (the effectiveness of cooperative lerarning implementation of floral material for calligraphy and ornamentation) To achieve the aim of the research scholar put the two zeros hypotheses: in light of the findings of the present research the researcher concluded a number of conclusions, including: -
1 - Sum strategy helps the learner to be positive in all the information and regulations, monitoring and evaluation during the learning process.
2 - This strategy helps the learner to use information and knowledge and their use in various educational positions, and to achieve better education to increase its ability to develop thinking skills and positive trends towards the article.
In light of this, the

Objective: To assess the role of tumour necrosis factor alpha level and genotyping in susceptibility to leishmaniasis.Method: The case-control study was conducted from March to July 2021 at Baqubah Teaching Hospital, Diyala, Iraq,and comprised patients of cutaneous leishmaniasis in group A and healthy controls in group B. The serum level andsingle nucleotide polymorphisms of tumour necrosis factor-alpha rs41297589 and rs1800629 were compared betweenthe groups. Data was analysed using SPSS 28.Results: Of the 150 subjects, there were 75(50%) in group A; 39(52%) males and 36(48%) females with mean age23.91±13.14 years. The remaining 75(50%) subjects were in group B; 38(50.7%) males and 37(49.3%) females withmean age 22.84±4.35 years.

The chemical properties of chemical compounds and their molecular structures are intimately connected. Topological indices are numerical values associated with chemical molecular graphs that help in understanding the physicochemical properties, chemical reactivity and biological activity of a chemical compound. This study obtains some topological properties of second and third dominating David derived (DDD) networks and computes several K Banhatti polynomial of second and third type of DDD.

    The aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.