Which of the following statements about a connected graph is always TRUE?         A path of edges exists between any two vertices of the graph.     There is an even number of vertices on the graph.     There is an even number of edges on the graph.     Every pair of vertices is joined by a single edge.

Q: An "X" in the table below indicates a direct train route between the corresponding cities. Is it…

A: There are 6 vertices. Let them be named by indicating the first letter of every city.

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A: 15 vertices and 105 edges

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Q: (a) Is there an undirected graph with 7 vertices such that five of the vertices have degree 3 and…

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A: Answer : (A)  Hence,   n = e + 1 is the true statement.

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A: Answer: 9 and 4

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A: This is a problem of Graph Theory.

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Q: Which statement is FALSE? a. A k-regular graph is also a complete graph  b. A bi-partite graph is…

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Q: If G is a graph, then the sum of its vertex degrees is nonnegative and even.

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A: We have to verify the given statements.

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A: I have given an answer in step 2.

Q: The given graph is strongly connected. b True or False True False

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Q: A graph is connected if and only if one vertex is neighbor to all other vertices O True O False

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Q: True or False: There exists a simple graph with 9 vertices each of degree 5. O True O False

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Q: 12. If G is a simple graph with vertices a, b, c, d, e and d(a) = d(b) = d(c) = 3 (d = degree), then…

A: Here we apply Hand-shaking lemma for simple graph.

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Q: Which one of the following statements is NOT true about this graph? A B F C E O There is a circuit…

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