Reliability Analysis in Communication Networks via Conditional Connectivity Parameters
Project no. 22840 · Status: Kapanmış · 2021
Summary
<p>We study communication networks' resilience against damage using several connectivity parameters. Throughout this project, novel results were obtained, and, moreover, a graph class with high potential for use in real-world problems was defined.</p><p> </p><p>There are three main categories of problems addressed in the project. First, uniform subset graphs, which also attract attention in different areas of mathematics, are examined. This family of graphs is also quite important in terms of intersecting families; the super-connectivity of this infinite graph class which models the case where three-element sets intersect in an element has been determined. Next, double generalized Petersen graphs are considered. The class's connectivity and super-connectivity have been determined. In recent years, this class has attracted considerable attention in the literature due to its members’ various algebraic properties.</p><p> </p><p>Finally, a novel hypercube architecture has been proposed. It also contains some well-known and extensively studied hypercube variants. This family's connectivity and super-connectivity have been determined. These results include previously known results. It is worth to note that we also get the connectivity of the novel examples of the newly defined family. The fact that this family can produce hybrid examples also increases the expected benefit of the project's future outputs.</p><p> </p><p>Different methods have been used in each of the three main sections of the project. This improves the project's potential contribution to the literature. For the uniform subset graphs, internally disjoint paths were determined based on various configurations. In double generalized Petersen graphs, elements that remain on different cycles are examined. In hypercube-like graphs, the proofs are completed using the recursive structure of the class.</p><p> </p><p><strong>Keywords:</strong> Graph Theory, Connectivity, Vulnerability, Conditional Connectivity</p>