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Discrete MathematicsConsider the following graph (a) Does a Hamiltonian path exist? If so describe it. If not say why not.20237mDiscrete MathematicsShow that a degree-constrained spanning tree of a simple graph in which each vertex has degree not exceeding 2 consists of a single Hamiltonian path in the graph.20225mDesign & Analysis of AlgorithmsHamiltonian path problem is ______? - (i) NP Problem - (ii) NP Complete - (iii) P Class Problem - (iv) N Class Problem20242mDesign and Analysis of Algorithms Design a system that finds the shortest paths between various locations in a city. The locations and roads are represented using a graph. What algorithm would you use if: (i) All roads have equal length (ii) Roads have varying lengths, but no negative lengths (iii) Some roads have negative lengths Justify your choices with suitable algorithms and reasoning.20247m
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