PART-C
7(a) Prove that "If a graph (connected or disconnected )has exactly two vertices
of odd degree , there must be a path joining these two vertices". (4)

(b) Discuss Elliptic Curve Arithmetic. (4)

(c)Prove that the subgroup of a Cyclic Group is Cyclic. (4)

8(a) Give examples of (i) Directed Graph (ii) Undirected Graph (iii) Simple Graph

(iv) Weighted Graph (4)

(b)What are decision Trees? Explain. (4)

(c) Discuss reciprocity. (4)

9(a) If in a Ring 'R' with Unity (xy)2 = Rya for all x, ye R then R is Commutative.
(4)

(b)Prove that the necessary & sufficient condition that a non-empty subset 'H' of
a Group 'G' be a Subgroup is a 5 11, ‏م‎ EH => abel E H. (4)

(c) State & Prove Euler's Theorem (4)

(2 x 12 = 24 marks)