  Demonstrating contextual correlations in quantum theory through the violation
of a non-contextuality inequality necessarily needs some ``contexts" and thus
assumes some compatibility relations between the measurements. As a result, any
self-testing protocol based on the maximal violation of such inequality is not
free from such assumptions. In this work, we propose temporal inequalities
derived from non-contextuality inequalities for multi-qubit systems without
assuming any compatibility relations among the measurements. We demonstrate
that the new inequalities can be maximally violated via a sequential
measurement scenario. Moreover, using the maximal violation of these temporal
inequalities we are able to certify multi-qubit graph states and the
measurements.
