Texture One Zero Dirac Neutrino Mass Matrix With Vanishing Determinant or Trace Condition

In the light of non-zero and relatively large value of rector mixing angle ($\theta_{13}$), we have performed a detailed analysis of texture one zero neutrino mass matrix $M_{\nu}$ in the scenario of vanishing determinant/trace conditions , assuming the Dirac nature of neutrinos. In both the scenarios, normal mass ordering is ruled out for all the six possibilities of $M_{\nu}$, however for inverted mass ordering, only two are found to be viable with the current neutrino oscillation data at $3\sigma$ confidence level. Numerical and some approximate analytical results are presented.