https://repository.cuk.ac.ke/handle/123456789/568 SCOM 2026-04-20T21:23:52Z https://repository.cuk.ac.ke/handle/123456789/1900 Unravelling DevOps Agile Methodologies: A Comprehensive Review of Recent Research Nyale, Duncan; Mbandu Angolo, Shem This study report offers a thorough analysis of current studies on DevOps Agile techniques. The study summarizes and dissects the major discoveries made in peer-reviewed literature, conference proceedings, and other academic publications. The article examines the most recent DevOps Agile practice trends and advances, as well as how they affect software development, testing, deployment, and operations. The analysis emphasizes the advantages of applying DevOps Agile approaches, including enhanced collaboration, faster time to market, and higher-quality software products. The paper also examines the challenges and potential limitations of DevOps Agile adoption, such as cultural resistance, lack of skills, and integration issues. Finally, the study concludes with recommendations for practical implications for software development teams and organizations seeking to implement DevOps Agile methodologies. The review provides valuable insights and guidance for researchers, practitioners, and decision-makers in the field of software engineering and information technology. Review of DevOps and Agile methods 2023-11-24T00:00:00Z https://repository.cuk.ac.ke/handle/123456789/1899 Enhancing Cyber Security: The Role of Networking, Coordination, and Trusted Information Sharing in Organizational Resilience Nyale, Duncan; Katila, Charles Organizations must take proactive measures to strengthen their cybersecurity posture as cyber-attacks continue to develop and become more sophisticated. Networking, coordination, and the sharing of trustworthy information among entities and organizations have become essential tactics for achieving this goal. This article gives a general overview of how networking, coordination, and trusted information sharing can improve an organization's cybersecurity posture. It covers the most recent advancements and trends in this field and analyses the advantages, difficulties, and best practices for putting these ideas into effect. The article's conclusion emphasizes the necessity of a cooperative, all-encompassing strategy for cybersecurity that incorporates networking, coordination, and reliable information exchange. Cybersecurity resilience through coordination and trusted information sharing 2024-09-01T00:00:00Z https://repository.cuk.ac.ke/handle/123456789/1898 Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets Gikunju, David Muriuki; Nyaga, Lewis Namu The study of suborbital graphs is a key area in group theory for it provides a graphical representation of a group action on a set. Moreover, it helps in understanding the combinatorial structures of the action of a group on a set. In this paper, we construct suborbital graphs based on the group action of the direct product of the symmetric group on Cartesian product of three sets through computation of the ranks and subdegrees of the group action. Suborbital graphs are constructed by the use of Sims theorem. The properties of the suborbital graphs are analyzed. In the study it is proven that the rank of the group action of direct product of the symmetric group acting on the Cartesian product of three sets is 8 for all n ≥ 2 and the suborbits are length 1, (n-1), (n-1), (n-1), (n-1)2, (n-1)2, (n-1)2, (n-1)3. We show that the suborbits of the group action are self-paired. Furthermore, it is demostrated that each graph has a girth of 3 for all n > 2 and suborbital graphs of the group action are undirected. It is shown that graphs Γ2 and Γ3 are regular of degree n-1, graphs Γ4, Γ5 and Γ6 of degree (n-1)2 and graph Γ7 is regular of degree (n-1)3. The suborbital graphs Γi(i=1, 2,…, 6) are disconnected, with the number of connected components equal to n2 while suborbital graph Γ7 is connected for all n > 2. Studies suborbital graphs under group actions 2024-10-18T00:00:00Z https://repository.cuk.ac.ke/handle/123456789/1897 Combinatorial Properties and Invariants Associated with the Direct Product of Alternating and Dihedral Groups Acting on the Cartesian Product of Two Sets Mokaya John, Victor; Nyaga, Lewis Namu; Gikunju, David Muriuki Group theory, an area in mathematics, has undergone extensive research, but not exhaustively. In group theory, especially symmetric groups have been studied in terms of properties and actions. In this research, two groups of the Symmetric Group (Alternating and Dihedral Groups) are studied in terms of their properties and also their direct product between them. Also, ordered sets are studied in this research where their Cartesian product is looked at. Finally, this research combines the direct product of two symmetric groups (alternating group and dihedral group) and the Cartesian product of two ordered sets (X×Y) by group action. This research therefore focuses on determining the combinatorial properties (transitivity and primitivity), invariants (ranks and subdegrees), and structures (suborbital graphs) of this group action. To accomplish this, orbit-stabilizer theorem is used to compute transitivity, block action concept is applied to determine primitivity, and Cauchy-Frobenius lemma is used to compute ranks and subdegrees. For n ≥ 3, it has been confirmed that the group action is transitive and also imprimitive. The rank of this group action is 6 and the subdegrees are obtained using the formula of Theorem 3.3. This research adds new concepts in group theory which will be useful in other areas like graph theory and also application in real life situations. Group action structures and invariants (alternating × dihedral) 2024-12-18T00:00:00Z