It has been tried to see to what extent the hypothesis of L.H. Kauffman conjecture can be weakened or whether it can be extended to links. By a diagrammatic approach it has been shown that the converse of the conjecture is not true. By associating LRGraphs with knots (links), we have not only established the validity of a part of the conjecture, but have also shown that the corresponding graphs have the same number of vertices, edges and regions.