Final answer:
To construct a connected bipartite graph, divide the vertices into two sets and connect them with edges. To construct a graph with a degree of 3 for a specific vertex, connect it to three vertices in the other set.
Step-by-step explanation:
A connected bipartite graph is a graph in which the vertices can be divided into two sets, and there are only edges between vertices in different sets. To construct a connected bipartite graph with the vertices M, N, O, P, Q, we can divide the vertices into two sets, for example, {M, O, Q} and {N, P}. Then, we can connect the vertices in the first set to the vertices in the second set with edges. For example, we can add the edges MO, OQ, and QN, as well as the edges MP and PO. This graph is connected because there is a path between any two vertices.
To construct a bipartite graph with a degree of 3 for vertex O, we can follow a similar procedure. We can divide the vertices into two sets, for example, {M, O, Q} and {N, P}. Then, we can add edges between O and three vertices in the second set. For example, we can add the edges ON, OP, and OQ. This graph is bipartite and O has a degree of 3 because it is connected to three vertices in the second set.