An independent vertex set of a graph $G$ is a subset of the vertices such that no two vertices in the subset has an edge in $G$.
A maximum independent vertex set is an independent vertex set containing the largest possible number of vertices for a given graph. A maximum independent vertex set is not equivalent to a maximal independent vertex set, which is simply an independent vertex set that cannot be extended to a larger independent vertex set.
The independence number of a graph is the cardinality of the maximum independent set.
In the given graph vertices $2,4,6$ and $8$ are connected to all other vertices and each of them form a maximal vertex set of size $1$ (addition of any other vertex is not possible). The maximal independence vertex set is of size (independence number) $4 - \color{magenta}{\{1,3,5,7\}}$
And there is no other independence vertex set of size $4$ which means the number of maximum independence set of the given graph is $1.$
