Decompositions of hypercube graphs into paths cycles and stars

Abstract

The current research of graph decomposition has been one of the newlinemost prominent areas of graph theory, since many combinatorial, algebraic newlineand other mathematical structures are linked to graph decomposition which newlinemakes their research a great theoretical importance. In addition to it, the results newlineof graph decomposition can be used in design of experiments, coding theory, newlineradio astronomy, X-ray crystallography, computer and communication newlinenetworks and in other fields. newlineThe significance of cube graphs is intensively studied in graph newlinetheory and the interest in hypercube graphs has been escalated by the recent newlineadvent of massively parallel computers whose structure is that of hypercube newlinegraphs. The hypercube graph is the generalization of a cube into more newlinedimensions. The hypercube graph topology proposes ample interconnection newlinestructures with large bandwidth capabilities, logarithmic diameter measures, newlineand extreme magnitude of fault tolerance. Another intriguing attribute of the newlinehypercube graph is its homogeneity and symmetry. It is understood that from newlinea topological point of view, the hypercube graph facilitates a perfect balance newlinebetween node connectivity, network diameter, and algorithm embeddability newlinewhich ultimately makes the programming easier. This balance makes the newlinehypercube graph suitable for a wide class of computationally extensive newlineproblems. newline