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- Prove that a complete bipartile graph Ks,s has (s−1)!s!/2 Hamiltonian walks for s >1Graph the limaçon. Limaçons with an inner loop r = 1/2 + cos uDraw the graph of the following map: xn+1= {3xn if x<1/3 {3(xn- 1/3)/2 if x>1/3 Show also that the periodic orbits are unstable and dense in the unit interval.
- Show that there is no hamiltonian path in Cay ({(1,0),(0,1)}: Z3 +Z2) from (0,0) to (2,0).A natural cubic spline S is defined byS0(x) = 1+B(x −1)−D(x −1)3, if 1 ≤ x < 2 S1(x) = 1+b(x−2) −3/4(x−2)2 + d(x−2)3, if 2 ≤ x ≤ 3If S interpolates the data (1, 1), (2, 1), and (3, 0), find B, D, b, and d.(Show your work) compute the girth of all generalized Coxeter graphs with parameter Pn,u,v where n is less or equal to12
- The complete graph of K12 is: Only Euler Only Hamiltonian Both NeitherConsider a bipartite graph with edges in E connecting members of the vertex bipartition S, T, and let weights Wi ≥ 0 be defined for vertices I S.I need solution about exercise 6 but need Hint. Consider the Laurent decomposition at each Z k, and use Exercise 5.
- (Show your work) prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are.Prove that If a connected planar simple graph has e edges and v vertices with v ≥ 3 and no circuits of length three, then e ≤ 2v − 4. (Show work)prove that the maximum girth of a generalized Coxeter graph is 12, no matter what its parameters are.