NIELIT 2017 July Scientist B (IT) - Section B: 7

Question

Which of the following statements is/are TRUE?

$S1$:The existence of an Euler circuit implies that an Euler path exists.

$S2$:The existence of an Euler path implies that an Euler circuit exists. 

• A. $S1$ is true.
• B. $S2$ is true.
• C. $S1$ and $S2$ both are true.
• D. $S1$ and $S2$ both are false.

Comments

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

Answer 1

An Euler circuit in a graph G is a simple circuit containing every edge of G exactly once
An Euler path in G is a simple path containing every edge of G exactly once.
An Euler path starts and ends at different vertices.
An Euler circuit starts and ends at the same vertex.

Euler path+ ends at the same vertex.= Euler circuit ,only s1 true

option A