Phenomenology of Trimaximal Mixing with One Texture Equality

We study neutrino mass matrices with one texture equality and the neutrino mixing matrix having either its first ( $\text{T}{\text{M}}_1$ ) or second ( $\text{T}{\text{M}}_2$ ) column identical to that of the tribimaximal mixing matrix. We found that out of total fifteen possible neutrino mass matrices with one texture equality, only six textures are compatible with $\text{T}{\text{M}}_1$ mixing and six textures are compatible with $\text{T}{\text{M}}_2$ mixing in the light of the current neutrino oscillation data. These textures have interesting implications for the presently unknown parameters such as the neutrino mass scale, effective Majorana neutrino mass, effective neutrino mass, the atmospheric mixing, and the Dirac- and Majorana-type CP violating phases. We, also, present the $S_3$ group motivation for some of these textures.