  In this paper, We investigate three-mode photon-added
Greenberger-Horne-Zeilinger (GHZ) entangled coherent states by repeatedly
operating the photon-added operator on the GHZ entangled coherent states. The
product of two Laguerre polynomials is demonstrated to be connected to the
normalizing constant. The influence of the operation on the non-classical and
non-Gaussian behavior of the GHZ entangled coherent states is investigated.
Sub-Poissonian statistics, such as Mandel's parameter and the negativity of the
Wigner function, show that non-classical properties can enhance GHZ entangled
coherent states. Finally, the occurrence of the anti-bunching phenomena in this
class of tripartite excited states is studied using the second-order
correlation function.
