Answer the following questions, each one is worth $4$ points:

Suppose that there are four employees in the computer support group of the School of Engineering of a large university. Each employee will be assigned to support one of four different areas: hardware, software, networking, and wireless. Suppose that Ping is qualified to support hardware, networking, and wireless; Quiggley is qualified to support software and networking; Ruiz is qualified to support networking and wireless, and Sitea is qualified to support hardware and software.

a$)$ Use a bipartite graph to model the four employees and their qualifications.

c$)$ If an assignment of employees to support areas so that each employee is assigned to one support area exists, find one.

Draw the graph represented by the following adjacency matrix and find the connectivity of such graph.

$\left[\begin{array}{cccc}1& 1& 1& 0\\ 0& 0& 1& 0\\ 1& 0& 1& 0\\ 1& 1& 1& 0\end{array}\right]$