Pre- provisional and predicate crisp sets relation and function, Fuzzy complement, Fuzzy union, fuzzy intersection combination of operations general Aggregation operation.

Crisp and fuzzy relations binary relations, Binary relations on a single set Equivalence and Similarity Relations, Compatibility or Tolerance Relations Cord rings, Marphisms, Fuzzy relation Equations.

Lattices semi group ring fields etc, Counting Techniques, pigeon, hole principa, infinite sets mathematical, induction permutations (with repetition etc), Generating functions, Recurrence Relations & their solution..

Graph, finite and infinite Graph, Incidence and degree, isolated vertex, pendent vertex and Null graph, Isomorphism, sub graph, walks, paths and circuits connected graphs, disconnected graphs and components, Euler graph operations on graph mare on Eular graph Hamiltonian, paths and circuits dictograph same type of diagraph and binary Relation, Eular Diagraphs trees with Directed Edges..

Inside once matrix, Sub matrices of A (G), circuit matrix fundamental circuit matrix and rank of B chromatic, Number, chromatic polynomial Four color Problem Five color Tearoom, General Application of graph in switching and coding theory in Electrical network Analysis and in operation research graph in computes programming.