The Texture One Zero Neutrino Mass Matrix With Vanishing Trace

In the light of latest neutrino oscillation data, we have investigated the one zero Majorana neutrino mass matrix $M_{\nu}$ with zero sum condition of mass eigen values in the flavor basis, where charged lepton mass matrix is diagonal. Among the six possible one-zero cases, it is found that only five can survive the current experimental data, while case with (1, 1) vanishing element of $M_{\nu}$ is ruled out, if zero trace condition is imposed at 3$\sigma$ confidence level (CL). Numerical and some approximate analytical results are presented.