A rectangular floor plan (RFP) is a floor plan in which plan's boundary and each room is a rectangle. First, the task is to generate all inner graphs on ‘n’ vertices for which Rectangular floor plan is possible. The idea is to first construct a path graph and then to add edges between two vertices if the length of the shortest path between them is found to be two. This way we will obtain different triangulated graphs and then we have to check various conditions on it to make sure if there exists a corresponding floor plan for it. Given a dual graph of an RFP, the second task is to add 4 more vertices to it so that it forms a maximal dual graph. This method is called “IO” where ‘I’ refers to the inner vertices and ‘O’ refers to the outer ones.The initial graph is referred to as the inner graph with n vertices and the final result as the outer graph with n+4 vetices. This method gives all possible non-isomorphic maximal graph for n+4 vertices for a given inner graph of n vertices.

A rectangular floor plan (RFP) is a floor plan in which plan's boundary and each room is a rectangle. In architectural design, the first step is to build a floor plan as per the adjacency constraints. Mathematically, the problem is to draw a rectangular floor plan(RPF) corresponding to the planar graph satisfying all the adjacency constraints; in which each rectangle corresponds to a vertex in the planar graph and connectivity of this rectangle is defined by the edges in the planar graph.In a rectangular floor plan (RFP) each room is rectangle along with its boundary. This conversion of planar graph into a rectangular floor plan is called Rectangular Dualization. Rectangular Dualization was originally introduced to generate rectangular topologies for floor planning of integrated circuits. A graph which is the dual graph of a rectangular floor plan is called rectangular floor plan graph.Rectangular floor plan graph is said to be maximal if drawing a rectangular floor plan is not possible of the graph obtained by adding any new edge to it.Two rectangular floor plans are said to be isomorphic if and only if one can be derived from the other using translation, rotation, reflection and scaling of the rooms in the RFP. In our work, we first studied various algorithms by which a maximal rectangular floor plan could be obtained on ‘n’ vertices. The first being introduced by Dr. Krishnendra Shekhawat for enumerating all maximal rectangular floor plan(MRFP) on n vertices by using the MRFP on ‘n-1’ vertices. Dr. shinichi Nakano also wrote a paper on Enumeration floor plans on n rooms which could be used to draw MRFP by adding four rooms to the outer boundary of RFP. As the time complexity for it being (n)! It couldn’t be used for enumeration of maximal RFP for larger than 8 vertices. Then we tried to come up with our own algorithm to enumerate MRFP for ‘n’+4 vertices by firstly drawing all dual graphs on ‘n’ vertices and then adding 4 boundaries to make a MRFP for n+4 vertices . We also used some of the conditions of the paper “Heuristic method to check the realisability of a graph into a rectangular plan” written by A. Recuero, M. Alvarez and O. Rio to check the realisability of inner graph.