Question

(a) determine the adjacency matrix for $k {3,5}$. \\ewline (b) how many walks (edges and vertices may repeat) of length $\ell$ are there between distinct vertices in c4? where $\ell$ is the specific value of: the last 2 digits in your student number added together. [hint: consider the adjacency matrix] \\ewline \\

Answer 1

To determine the adjacency matrix for k {3,5}, we need to understand what k {3,5} represents. The adjacency matrix is a 3x5 matrix where each vertex in the first set is connected to every vertex in the second set.

Step-by-step explanation:

To determine the adjacency matrix for k {3,5}, we first need to understand what k {3,5} represents. The notation k {3,5} refers to a complete bipartite graph where the first set of vertices contains 3 elements and the second set contains 5 elements. In an adjacency matrix, rows and columns represent the vertices, and the entries indicate whether there is an edge between the vertices or not.

For k {3,5}, we would have a 3x5 matrix. The first three rows will correspond to the vertices in the first set, and the next five rows will correspond to the vertices in the second set. The entries in the matrix will be 1 if there is an edge between the vertices and 0 if there isn't. In this case, each vertex in the first set is connected to every vertex in the second set, so the adjacency matrix will be:

| 0 0 0 1 1 |

| 0 0 0 1 1 |

| 0 0 0 1 1 |

Keywords: adjacency matrix, bipartite graph, vertices, edges