If G is a simple graph with n-vertices and n>=3, the condition for G has a Hamiltonian circuit is __________(a) the degree of each vertex is at most n/2(b) the degree of each vertex is equal to n(c) the degree of every vertex is at least n+1/2(d) the degree of every vertex in G is at least n/2I have been asked this question in class test.The above asked question is from Trees topic in chapter Trees of Discrete Mathematics

If G is a simple graph with n-vertices and n>=3, the condition for G h

1.	If G is a simple graph with n-vertices and n>=3, the condition for G has a Hamiltonian circuit is __________(a) the degree of each vertex is at most n/2(b) the degree of each vertex is equal to n(c) the degree of every vertex is at least n+1/2(d) the degree of every vertex in G is at least n/2I have been asked this question in class test.The above asked question is from Trees topic in chapter Trees of Discrete Mathematics
Answer» The correct option is (d) the degree of EVERY VERTEX in G is at least n/2 The best explanation: A simple circuit in a graph G that PASSES through every vertex exactly once is CALLED a Hamiltonian circuit. If there is a vertex of degree ONE in a graph then it is impossible for it to have a Hamiltonian circuit. If G is a simple graph with n-vertices and n>=3 such that the degree of every vertex in G is at least n/2, then G has a Hamiltonian circuit.

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