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If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if
(i) deg(v) ≥n/3 for each vertex v
(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.
(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 2
  • a)
    (i) and (iii) only
  • b)
    (ii) and (iii) only
  • c)
    (iii) only
  • d)
    (ii) only
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If a graph (G) has no loops or parallel edges and if the number of ver...
Hamiltonian graph:
A Hamiltonian graph is one which contain a Hamiltonian cycle. A Hamiltonian cycle is a cycle in which each vertex is visited exactly once.
Properties of Hamiltonian graph:
(1) A graph has a Hamiltonian circuit if each vertex has degree >=3
(2) If G= (V, E) has n>=3 vertices and every vertex has degree >=n/2, then G has a Hamilton circuit
(3) If G is a graph with n vertices and n>=3, also deg(u) + deg(v) >=n, if u and v are not connected by an edge, then G has a hamiltonion circuit.
(4) E(G) = ½(n - 1)(n - 2) + 2
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If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if(i) deg(v) ≥n/3 for each vertex v(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 2a)(i) and (iii) onlyb)(ii) and (iii) onlyc)(iii) onlyd)(ii) onlyCorrect answer is option 'D'. Can you explain this answer?
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If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if(i) deg(v) ≥n/3 for each vertex v(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 2a)(i) and (iii) onlyb)(ii) and (iii) onlyc)(iii) onlyd)(ii) onlyCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if(i) deg(v) ≥n/3 for each vertex v(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 2a)(i) and (iii) onlyb)(ii) and (iii) onlyc)(iii) onlyd)(ii) onlyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if(i) deg(v) ≥n/3 for each vertex v(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 2a)(i) and (iii) onlyb)(ii) and (iii) onlyc)(iii) onlyd)(ii) onlyCorrect answer is option 'D'. Can you explain this answer?.
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