We obtain the existence results of ground state sign-changing solutions and
ground state solutions for a class of second order elliptic equation with
logarithmic nonlinearity on a locally finite graph G=(V,E), and obtain the
sign-changing ground state energy is larger than twice of the ground state
energy. The method we used is a direct non-Nehari manifold method in [X.H.
Tang, B.T. Cheng. J. Differ. Equations. 261(2016), 2384-2402.