$S_{1}$ : I teach algorithms and maths.
$S_{2}$ : My professor teaches maths, electronics and computer science.
$S_{3}$ : I have a student of maths.
$S_{4}$ : Algorithm is a part of computer science.
$S_{5}$ : Maths students know computer science.
What would be the chromatic number of a graph, vertices of which are the actors/entities that are involved in the sentences $S_{1}$ to $S_{5}$ and edges to represent the associations/relationships amongst the entities/actors as expressed in the sentences $S_{1}$ to $S_{5}$ above ?
- $2$
- $3$
- $4$
- None of these