A high school math department offers a total of $5$ classes: MTH$01,$ MTH$02,$ MTH$03,$ MTH$04,$ and MTH$05.$ However, the following courses cannot be taught at the same time due to staffing limits:

$$ MTH$01$ conflicts with MTH$02,$ MTH$05$

$$ MTH$02$ conflicts with MTH$01,$ MTH$03$

$$ MTH$03$ conflicts with MTH$02,$ MTH$04$

$$ MTH$04$ conflicts with MTH$03,$ MTH$05$

$$ MTH$05$ conflicts with MTH$01,$ MTH$04$

We want to know the minimum number of time slots needed to teach these classes. What information about the graph would answer this question?

Group of answer choices

number of vertices

number of edges

chromatic index

chromatic number