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The following simple undirected graph is referred to as the Peterson graph.
Which of the following statements is/are TRUE?
- a)The chromatic number of the graph is 3.
- b)The graph has a Hamiltonian path.
- c)The following graph is isomorphic to the Peterson graph.
- d)The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
Correct answer is option 'A,B,C'. Can you explain this answer?
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The following simple undirected graph is referred to as the Peterson g...
Option 1:The chromatic number of the graph is 3.
True, the Chromatic number of the Peterson graph is 3. We colour the graph with three colours (B, G, R).
True, the Chromatic number of the Peterson graph is 3. We colour the graph with three colours (B, G, R).
Option 2: The graph has a Hamiltonian path.
True, A Hamilton Path is a path that goes through every vertex of a graph exactly once. A Hamilton Circuit is a Hamilton path that begins and ends at the same vertex.
The Peterson graph has a Hamiltonian path but not a Hamiltonian cycle.
From above graph,
Hamiltonian path= F-B-A-I-E-D-H-G-J
True, A Hamilton Path is a path that goes through every vertex of a graph exactly once. A Hamilton Circuit is a Hamilton path that begins and ends at the same vertex.
The Peterson graph has a Hamiltonian path but not a Hamiltonian cycle.
From above graph,
Hamiltonian path= F-B-A-I-E-D-H-G-J
Option 3:The following graph is isomorphic to the Peterson graph.
True, If the adjacency matrices of two graphs are identical, they are said to be isomorphic or If the respective sub-graphs created by removing certain vertices of one graph and their corresponding images in the other graph are isomorphic, then the two graphs are isomorphic.
The given graph is isomorphic to Peterson's graph.
True, If the adjacency matrices of two graphs are identical, they are said to be isomorphic or If the respective sub-graphs created by removing certain vertices of one graph and their corresponding images in the other graph are isomorphic, then the two graphs are isomorphic.
The given graph is isomorphic to Peterson's graph.
Option 4: The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)
False, A vertex independent set is a set of vertices that are not adjacent. Maximal vertex independent set is a set in which we cannot add one more vertex to it. So, the largest independent set of the Peterson graph is 4.
Hence the correct answer is options 1,2 and 3.
False, A vertex independent set is a set of vertices that are not adjacent. Maximal vertex independent set is a set in which we cannot add one more vertex to it. So, the largest independent set of the Peterson graph is 4.
Hence the correct answer is options 1,2 and 3.
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The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are TRUE?a)The chromatic number of the graph is 3.b)The graph has a Hamiltonian path.c)The following graph is isomorphic to the Peterson graph.d)The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)Correct answer is option 'A,B,C'. Can you explain this answer?
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The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are TRUE?a)The chromatic number of the graph is 3.b)The graph has a Hamiltonian path.c)The following graph is isomorphic to the Peterson graph.d)The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)Correct answer is option 'A,B,C'. 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 The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are TRUE?a)The chromatic number of the graph is 3.b)The graph has a Hamiltonian path.c)The following graph is isomorphic to the Peterson graph.d)The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)Correct answer is option 'A,B,C'. 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 The following simple undirected graph is referred to as the Peterson graph.Which of the following statements is/are TRUE?a)The chromatic number of the graph is 3.b)The graph has a Hamiltonian path.c)The following graph is isomorphic to the Peterson graph.d)The size of the largest independent set of the given graph is 3. (A subset of vertices of a graph form an independent set if no two vertices of the subset are adjacent.)Correct answer is option 'A,B,C'. Can you explain this answer?.
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