Euler & Hamiltonian Circuit - ALL Previous Exam Questions | GATE, TIFR, NET, NIELIT | with NOTES

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UGC NET CSE | December 2010 | Part 2 | Question: 2: https://gateoverflow.in/66493/ugc-net...
An undirected graph possesses an eulerian circuit if and only if it is connected and its vertices are
All of even degree
All of odd degree
Of any degree
Even in number

ISRO2016-5: https://gateoverflow.in/55688/isro2016-5
A given connected graph G is a Euler Graph if and only if all vertices of G are of
same degree
even degree
odd degree
different degree

GATE IT 2008 | Question: 27: https://gateoverflow.in/3317/gate-it-...
G is a simple undirected graph. Some vertices of G are of odd degree. Add a node v to G and make it adjacent to each odd degree vertex of G. The resultant graph is sure to be
regular
complete
Hamiltonian
Euler

UGC NET CSE | August 2016 | Part 2 | Question: 5: https://gateoverflow.in/69380/ugc-net...
Given the following graphs :
Which of the following is correct ?
G1 contains Euler circuit and G2 does not contain Euler circuit.
G1 does not contain Euler circuit and G2 contains Euler circuit.
Both G1 and G2 do not contain Euler circuit.
Both G1 and G2 contain Euler circuit.

TIFR CSE 2020 | Part B | Question: 13: https://gateoverflow.in/333134/tifr-c...
Let G be an undirected graph. An Eulerian cycle of G is a cycle that traverses each edge of G exactly once. A Hamiltonian cycle of G is a cycle that traverses each vertex of G exactly once. Which of the following must be true?
Checking if G has a Eulerian cycle can be done in polynomial time
Deciding if G has a Hamiltonian cycle is not NP-complete
If G has an Eulerian cycle, then it has a Hamiltonian cycle
A complete graph always has both an Eulerian cycle and a Hamiltonian cycle
All of the other statements are true

TIFR CSE 2016 | Part B | Question: 9: https://gateoverflow.in/98001/tifr-cs...
Which of the following graphs DOES NOT have an Eulerian circuit? (Recall that an Eulerian circuit in an undirected graph is a walk in the graph that starts at a vertex and returns to the vertex after traveling on each edge exactly once.)
The graph on vertex set with edge set

NIELIT 2017 July Scientist B (IT) - Section B: 7: https://gateoverflow.in/336428/nielit...
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.
S1 is true.
S2 is true.
S1 and S2 both are true.
S1 and S2 both are false.

NIELIT 2017 July Scientist B (CS) - Section B: 12: https://gateoverflow.in/336363/nielit...
The following graph has no Euler circuit because
It has 7 vertices.
It is even-valent (all vertices have even valence).
It is not connected.
It does not have a Euler circuit.

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Content of this video:

00:00:00 - ALL Euler, Hamiltonian Questions
00:01:02 - UGC NET CSE | December 2010 | Eulerian Circuit
00:02:56 - ISRO2016-5 - Euler Graph
00:04:22 - GATE IT 2008 | Question: 27 - Euler, Hamiltonian, Regular, Complete
00:25:12 - UGC NET CSE | August 2016 - Euler Circuit
00:30:57 - TIFR CSE 2020 | Part B | Question: 13 - Hamiltonian Cycle, Eulerian Cycle
00:51:45 - TIFR CSE 2016 | Part B | Question: 9 - Eulerian Circuit
01:09:58 - NIELIT 2017 July Scientist B (IT) - Section B: 7 - Euler Circuit, Euler Path
01:18:09 - NIELIT 2017 July Scientist B (CS) - Section B: 12 - Euler Circuit
01:23:58 - Few More Questions on Euler Circuits, Euler Path

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