In contrast to the different approaches currently adopted for generating basic and side-split subcolumn distillation sequence for separating zeotropic multicomponent feed mixture, we present a unified graphical method applicable towards both basic and side-split subcolumn distillation sequence. For a given number of components in the feed mixture, we enforce constraints on a base graph to eliminate violations of conservation principles and to preclude distillation sequences that demand higher heat duty in all appraised practical scenarios. A compact set of algebraic constraints is transfixed using the graph counterpart for generating basic-only distillation configurations. These algebraic constraints utilize binary variables to quantify existence of submixture streams and this considerably reduces the number of variables in generating distillation sequences. We also suggest extension of the formulation to enable the exploration of thermally coupled configurations.