QQuestionMathematics
QuestionMathematics
"Such a path that begins and ends at the same vertex and passes through all other vertices exactly once is called a _________________ circuit.
a) Euler
b) Hamiltonian
c) Closed
d) Bipartite"
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Answer
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Step 1:: Identify the type of path described.
A path that begins and ends at the same vertex and passes through all other vertices exactly once is called a Hamiltonian circuit.
Step 2:: Understand the definition of a Hamiltonian circuit.
A Hamiltonian circuit is a path in a graph that visits every vertex exactly once and returns to the starting vertex. Not all graphs have Hamiltonian circuits, but some do, and they are an important concept in graph theory.
Step 3:: Identify the correct answer.
Based on the definition and the given choices, the correct answer is: b) Hamiltonian
Final Answer
The correct answer is (b) Hamiltonian.
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