Algorithm to Find Clique Graph

Let V = {1, 2, 3, …, n} be the vertex set of a graph G, ℘ (V) the powerset of V and A ∈ ℘ (V ). Then A can be represented as an ordered n-tuple (x₁x₂x₃…x_n) where x_i = 1 if i ∈ A, otherwise x_i = 0 (1≤ i ≤ n). This representation is called binary count (or BC) representation of a set A and denoted as BC(A). Given a graph G of order n, every integer m in S = {0, 1, 2, …, 2ⁿ-1} corresponds to a subset A of V and vice versa. In this paper we introduce and discuss a sequential algorithm to find the clique graph K(G) of a graph G using the BC representation.