NIELIT 2017 July Scientist B (CS) - Section B: 12

Question

The following graph has no Euler circuit because

• A. It has $7$ vertices.
• B. It is even-valent (all vertices have even valence).
• C. It is not connected.
• D. It does not have a Euler circuit.

Answer 1

The above given Graph is not connected that's why Euler circuit doesn't exist.

Answer 2

An undirected graph has an Eulerian cycle if and only if every vertex has even degree, and all of its vertices with nonzero degree belong to a single connected component.

Answer 3

A. Makes no sense

B. This is one of the condition for circuit being euler's circuit.

C. Even disconnected graph can be euler circuit but the the vertices which aren't part of main component shouldn't have any edge between them.

C is most appropriate option. 

Image Source: http://mathonline.wikidot.com/isolated-vertices-leaves-and-pendant-edges

Comments

How can a disconnected graph be an Euler circuit?

An Euler circuit in a graph G is a simple circuit containing every edge of G.

If the graph is disconnected it's impossible to contain all the edges.

Alright, I understood it. Sorry 😅