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Q1.

a) State and prove the Euler’s formula for a connected planar graph G = (V, E). As well prove that if |V| > 2, then |E| ≤ 3|V| - 6

b) Prove that a simple graph is connected if and only if it consists of a spanning tree.

c) State the Kuratowski’s Theorem. For what purpose this theorem is employed? Show by an illustration, how this theorem is employed.

Give an illustration of a graph which you prove to be non-planar by using this theorem.

Q2.

a. What do you mean by the term Binary Search Tree (BST)? Construct a BST for the given sequence of numbers.

45, 32, 90, 34, 68, 72, 15, 24, 30, 66, 11, 50, 10

Traverse the BST so made in the Post-order.

b) Illustrate the difference between a spanning tree and a minimum spanning tree. Apply Prim’s algorithm on the given graph to find out minimum spanning tree.

160_minimum spinning tree.jpg

Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M910277

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