Let $\mathfrak{A}=\{1,2,\dots,8\}$ and construct a graph as follows. Let the vertices of the graph be the set of all $A=(\{a,b,c\},\{d,e\})$ where $a,b,c,d,e\in \mathfrak{A}$ are distinct. Two vertices $(\{a,b,c\},\{d,e\})$ and $(\{f,g,h\},\{k,l\})$ are adjacent if $\{a,b,c\}=\{f,g,h\}$ and $\{a,b,c,d,e\} \cap \{f,g,h,k,l\}=\{a,b,c\}$ or if $\{d,e\}=\{k,l\}$ and $\{a,b,c,d,e\} \cap \{f,g,h,k,l\}=\{d,e\}$.

My question is what is the independence number of this graph?

Recall that the independence number of a graph is the maximum number of vertices with no edge between them.