A Hamilton graph is a graph that has a Hamiltonian cycle ,which means a cycle exists in this graph in which you can visit every vertex of graph exactly once .
My observation is : - Say for a(any) Hamilton graph of 100 vertices , the value of its maximum independent set will be 50 .
Can somebody prove it or verify it ?
This is plainly false. The complete graph on $n>2$ vertices is Hamiltonian but has maximum independent set size of only $1$.
However, if a Hamiltonian graph on $2n$ vertices is bipartite, then it is true that its maximum independent set size is $n$ (take one bipartition).