Consider the populations of 16 isolated Pacific islands (they do not know the existence of one another). There is a total of 4096 people on those 16 islands. Consider the social graph G as described in class (i.e. with 4096 vertices) where an edge connects vertices if the persons know each other only. What is the correct statement about L, the graph Laplacian of G? OL has no zero eigenvalues. L has exactly 16 eigenvalues of L are zero. OL has 256 zero eigenvalues. OL has at least 16 eigenvalues of L are zero.

Q: 8. Show the adjacency matrix for this graph, where vertex i is represented by the i-th row and i-th…

A: The adjacency matrix A of a graph with n vertices is defined by numbering the vertices, say from 1…

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Q: Problem 54: Prove of find a counter example: If there are exactly 2 nodes in G with odd degree there…

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A: The problem is from the graph theory.

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A: We use the properties of directed graph and walk of lengths.

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Q: 5. Prove Corollary 3.6: "Let u and v be vertices of a 2-connected graph G. Then there is a cycle of…

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