UGC NET CSE | December 2015 | Part 2 | Question: 2

Question

Which of the following statement(s) is/are false?

1. A connected multigraph has an Euler Circuit if and only if each of its vertices has even degree.
2. A connected multigraph has an Euler Path but not an Euler Circuit if and only if it has exactly two vertices of odd degree.
3. A complete graph (Kn) has a Hamilton Circuit whenever n $\geq$ 3.
4. A cycle over six vertices (C6) is not a bipartite graph but a complete graph over 3 vertices is bipartite.

Codes :

• A. i only
• B. ii and iii
• C. iii only
• D. iv only

Answer 1

An Euler circuit of a graph G is a simple circuit that contains every edge of G.
A connected multigraph has an Euler circuit if and only if each of its vertices has even degree.

A connected multigraph has an Euler path but not an Euler circuit if and only if it has exactly two vertices of odd degree.

A complete graph K_n has a Hamilton circuit for n≥3.

Cycle graphs with an even number of vertices are bipartite.

Thus C 8 also can be birpatite.

D  is false

Answer D