Reliability Measures in Interconection Networks and Distance Based Topological Indices in Cheminformatics

Abstract

newline Graph theory and mathematical models serve as an essential component of newlineartificial intelligence and networking in theoretical computer science. This thesis newlineexamines the computational complexity of a few optimization problems in the newlinefield of AI and networking which can be modeled as graph theoretical problems. newlineNumerous applications of graph theory can be discovered in the field of com- newlineputer science. The creation of graph algorithms plays a key role in computer newlineapplications for graph theory. Graph models help in the design and analysis newlineof algorithms for the underlying computational problems. These algorithms are newlineused to resolve theoretical issues with graphs, which the intern utilised to resolve newlinerelevant computer science application issues. There are several algorithms in the newlineliterature to compute graph properties, shortest path/distances in the graphs, newlinespanning trees of a graph, articulation points, and searching for specific nodes. newlineThe thesis s content is split into three segments: graph theoretical techniques, newlinealgorithms and programming. newlineIn the context of this study, the three key parameters related to interconnec- newlinetion networks have been examined. The initial parameter we ll explore involves newlinetopological indices used to characterize specific graph theoretical networks that newlineare of significance in the fields of chemistry and biology. The graph theoretical newlinetechniques will apply topological indices (descriptors) for the purpose of thorough newlineunderstanding of the connections between the physicochemical characteristics and newlinethe behaviour of nanomaterials in biological systems. The current study explored newlinethe significance of several graphs of biological interest, such as pandemic trees, newlineCayley trees, Christmas trees, and the corona product of Christmas trees and newlinepaths, in the context of the worldwide coronavirus 2019 (COVID-19) outbreak. newlineThe findings demonstrated how the graph theoretical network might be used to newlineanalyse virological data, i.e., to determine COVID-19 s formation and establish newlinecontainment strategies to prevent the disease from spreading by proving some newlinegeneral structural results about the progression of the pandemic through a topo- newlinelogical characterization of some graphs of biological interest. This data is crucial newlinewhen examining or monitoring the spread of disease.