Discrete Structures

2/3 3. Given the adjacency matrix M in Question 2c, compute M2. What do the numbers in the resulting matrix represent? Look at the corresponding graph of the M that you drew in Question 2c. (Aside: What do the entries of M3 represent? M*?) 4. Given a graph G with n vertices, where n is even, prove that if every vertex has degree n/2 +1, then G must contain a 3-cycle (a clique of size 3). A 3-cycle is a set of 3 vertices, a, b, c such that ab is an edge, be is an edge and ac is an edge. 2/3 3. Given the adjacency matrix M in Question 2c, compute M2. What do the numbers in the resulting matrix represent? Look at the corresponding graph of the M that you drew in Question 2c. (Aside: What do the entries of M3 represent? M*?) 4. Given a graph G with n vertices, where n is even, prove that if every vertex has degree n/2 +1, then G must contain a 3-cycle (a clique of size 3). A 3-cycle is a set of 3 vertices, a, b, c such that ab is an edge, be is an edge and ac is an edge