Question

Suppose that the graph G has a Hamiltonian circuit. Then, G has a subgraph H with thefollowing property:(a) Every vertex of H has degree 2(b) Every vertex of H has degree 3(c) Every vertex of H has degree 5(d) Every vertex of H has degree 1​

Answer 1

Answer:

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Answer 2

Properties of  subgraph H of the Hamiltonian circuit

Explanation:

• In a mathematical field of  the graph theory, a Hamiltonian path is a path in n undirected or directed graph that reaches each vertex exactly once.
• The Hamiltonian cycle is a Hamiltonian path.
• Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete.

• H contains every vertex of G
• H is connected
• H has the same number of edges as vertices
• Every vertex of H has degree 2

Correct Question is -

Suppose that the graph G has a Hamiltonian circuit. Then, what properties will a subgraph H have ?