Example 2.1.3 Let's calculate the adjacency matrix for the graph from Example 1.7.1 drawn again. below. We consider the vertices in alphabetical order. Since there are edges between A and B, A and C, and A and E, in the first row for A we have a 1 in the 2nd, 3rd, and 5th column and Os elsewhere. B E D A B C D E ABCDE 011011 101 10 1 10 10 01100 10000 4. (a) Write the adjacency matrix for the complete graph K, and describe the general pattern for the adjacency matrix of K, for n 2 1. (b). Write the adjacency matrix for the complete bipartite graph K3 and describe the general pattern for the adjacency matrix of Km for n. m 2 1. 5. (a) Write the adjacency matrix for cycle C and describe the general pattern for the adjacency matrix of C for n 2 3. (b) Write the adjacency matrices for wheel W, and explain how to get the adjacency matrix of W, using the matrix for Cn. Hint: see how the matrix of W4 includes the matriz of C? A graph is regular if all of its vertices have the same degree. If a graph is regular with all vertices of degree r, we say the graph is r-regular. For example, the 4-cycle C4 is 2-regular whereas the complete graph K4 is 3-regular. 6. Which of these graphs are regular? Explain. Note: it might depend on n or m. (a) Cycle Cn (b) Path P (c) Complete Kn (d) Bipartite Km,n