Question: Consider the Petersen graph G=(V,E) given in Figure 1 . Figure 1: The Petersen graph with 10 nodes. The stable number of the Petersen graph

Consider the Petersen graph G=(V,E) given in Figure 1 . Figure

Consider the Petersen graph G=(V,E) given in Figure 1 . Figure 1: The Petersen graph with 10 nodes. The stable number of the Petersen graph is (G)=4. a) Write down the vertex set V, the edge set E and the adjacency matrix A for the Petersen graph. b) Formulate the maximum stable set problem as an integer programming problem. Solve its linear programming (LP) relaxation using CVX or CVXPY and report its optimal value. What is the relationship between this value and (G) ? c) Formulate the Lovsz semidefinite program (SDP) relaxation, solve it using CVX or CVXPY, and report its optimal value. What is the relationship between this value and (G)? d) What can you say about the optimal solutions of the LP and SDP relaxations? Which one is of better quality and why

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