A Study on Various Parameters of Interconnection Network k9 c9

Abstract

Graph theory has applications in various fields, including computer science (networks, social newlinenetworks, algorithms), transportation (route planning), biology (protein-protein interaction newlinenetworks), and many others. Graph theory provides a powerful framework for modeling newlineand solving problems related to relationships and networks. It has a wide range of practical newlineapplications and is a fundamental topic in both mathematics and computer science. It is highly newlineapplicable in the context of interconnection networks for computer systems. newlineThese networks are vital components in various computing environments, including data newlinecenters, supercomputers, and distributed systems. It allows engineers and researchers to model newlinenetwork structures, develop efficient routing strategies, assess fault tolerance, and ultimately newlineensure that these networks meet the performance requirements of modern computing systems. newlineOur thesis focuses on various graph parameters, one such parameter is embedding. newlineGraph embedding techniques and algorithms are applied to solve specific problems or gain newlineinsights into the structure and relationships within graphs. The goal is to find a suitable mapping newlinethat preserves the relevant properties of the original graph or network and embed those newlineproperties into the host network without much loss of time or cost. The second parameter, our newlinethesis deals with is graph colouring. newline Colouring refers to the assignment of colours to the vertices (or nodes) of a graph in newlinesuch a way that no two adjacent vertices share the same color. In general, finding the chromatic newlinenumber of an arbitrary graph is known to be an NP-hard problem. It has a wide range of newlinepractical applications in real-world problem-solving, including scheduling, map coloring, and newlineregister allocation in computer compilers. Researchers and computer scientists continue to develop newlineand refine algorithms for colouring graphs to address complex scheduling and resource newlineallocation challenges. newlineAnother parameter, we focus on in this thesis is pancyclicity. Pancyclicity is a