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Discrete MathematicsDoes an Eulerian path exist? If so describe it. If not say why not.20237mDesign & Analysis of AlgorithmsHamiltonian path problem is ______? - (i) NP Problem - (ii) NP Complete - (iii) P Class Problem - (iv) N Class Problem20242mDiscrete 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 and Analysis of Algorithms Apply the backtracking approach and find the Hamiltonian cycle for the graph given in the form of matrix. Show all the steps to find the cycle. | | A | B | C | D | E | F | |---|---|---|---|---|---|---| | A | 0 | 1 | 1 | 0 | 0 | 1 | | B | 1 | 0 | 1 | 1 | 0 | 0 | | C | 1 | 1 | 0 | 0 | 1 | 0 | | D | 0 | 1 | 0 | 0 | 1 | 0 | | E | 0 | 0 | 1 | 1 | 0 | 1 | | F | 1 | 0 | 1 | 0 | 1 | 0 |202310m