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Consider the following statement about the planarity of the graph.
(1) The number of regions (r) in a graph G (V, E) can be given by Euler formula r = E + V – 2
(2) If G is a connected planar simple graph with e edges and v vertices, where v >= 3 then
(e <= 3v="" –="">
(3) If in a planar graph G (v, e) there is a cycle with 4 or more vertices then (e <= 2v="" –="">
(4) Bipartite can’t have odd length cycles.
The number of correct statements is ________________?
Correct answer is '3'. Can you explain this answer?
Verified Answer
Consider the following statement about the planarity of the graph.(1)...
Statement 1 is false, because the Euler formula is r = E – V + 2.
Statement 2 and statement 3 are true, they are the corollary of the Euler formula. To get these, for statement 2, put (2e/3) >= r in the Euler formula.
To get statement 3, put (2e / 4) >= r, as the degree of every region will be greater than 4.
Statement 4 is also true. Just try to draw a bipartite graph that is having odd length cycle. And you will understand it.
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Consider the following statement about the planarity of the graph.(1) The number of regions (r) in a graph G (V, E) can be given by Euler formula r = E + V – 2(2) If G is a connected planar simple graph with e edges and v vertices, where v >= 3 then(e (3) If in a planar graph G (v, e) there is a cycle with 4 or more vertices then (e (4) Bipartite can’t have odd length cycles.The number of correct statements is ________________?Correct answer is '3'. Can you explain this answer?
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Consider the following statement about the planarity of the graph.(1) The number of regions (r) in a graph G (V, E) can be given by Euler formula r = E + V – 2(2) If G is a connected planar simple graph with e edges and v vertices, where v >= 3 then(e (3) If in a planar graph G (v, e) there is a cycle with 4 or more vertices then (e (4) Bipartite can’t have odd length cycles.The number of correct statements is ________________?Correct answer is '3'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statement about the planarity of the graph.(1) The number of regions (r) in a graph G (V, E) can be given by Euler formula r = E + V – 2(2) If G is a connected planar simple graph with e edges and v vertices, where v >= 3 then(e (3) If in a planar graph G (v, e) there is a cycle with 4 or more vertices then (e (4) Bipartite can’t have odd length cycles.The number of correct statements is ________________?Correct answer is '3'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statement about the planarity of the graph.(1) The number of regions (r) in a graph G (V, E) can be given by Euler formula r = E + V – 2(2) If G is a connected planar simple graph with e edges and v vertices, where v >= 3 then(e (3) If in a planar graph G (v, e) there is a cycle with 4 or more vertices then (e (4) Bipartite can’t have odd length cycles.The number of correct statements is ________________?Correct answer is '3'. Can you explain this answer?.
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