Which of the following statement/s is/are true or false? * Statement I: With Hamilton cycle, every edge must be used. Statement II: With Euler tour, every vertex mUst be used. Statements I and II are both True Statement I is True while statement Il is False Statement I is False while statement II is True Both statements are False

Harrison Mills

Harrison Mills

Answered question

2022-09-19

Which of the following statement/s is/are true or false? *
Statement I: With Hamilton cycle, every edge must be used. Statement II: With Euler tour, every vertex mUst be used.
Statements I and II are both True
Statement I is True while statement Il is False
Statement I is False while statement II is True
Both statements are False

Answer & Explanation

Jacey Humphrey

Jacey Humphrey

Beginner2022-09-20Added 7 answers

Step 1
A Hamiltonian cycle is a closed loop on a graph where every node (vertex) is visited exactly once
Notice that the circuit only has to visit every vertex once; it does not need to use every edge.
So, Statement I is false
Step 2
An Euler tour ( or Eulerian cycle , Eulerian circuit ) in an undirected graph is a cycle that uses each edge exactly once
A graph is an Euler tour if and only if every vertex has even degree. So it uses every vertex twice
So Statement II is True
Third option is correct

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