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: If a simple graph G is having 15 vertices and 5 edges then its complement graph G will have None of…

A: 15 vertices and 105 edges

Q: 1. Is there a connected graph whose degree are: a. 5, 3, 2, 2, 2, 1, 1

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: can you please provide explanations

A: Possible: Graph with 5: 3 vertices of degree 2 and 2 vertices of degree 1. Impossible: Graph with 5:…

Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: this graph connected? O Connected ONot Connected

A: Note that the graph is said to be connected if the pair of any two vertices is connected by a path.

Q: Are the following statements true or false? ? 1. K5 is planar 2. K2,3 is not planar 3. K4,5 is…

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Q: number

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Q: The graph G is a planar connected graph. It has 25 edges, and 9 faces. How many vertices does G…

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Q: Draw a directed graph consisting of five nodes, each of which is path connected to every other node…

A: please see the next step for solution

Q: Determine all bipartite graphs G whose complement G is also bipartite.

A: Let G be bipartite, with bipartitions: B1 and B2. Then any three vertices in B1 will form a triangle…

Q: Consider the graph below with vertex set {a,b,c,d,e,f}. The above graph is ---Select--- --Select---…

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Q: A graph thát iš connected and has no circuits is called a/an For such a graph, • every edge is a/an…

A: Remark: Connected graph: A graph is called connected if there is a path between every pair of…

Q: Which statement is FALSE? ) The sum of odd degrees always equals the sum of even degrees ) The sum…

A: ANSWER :

Q: 13. Show by example that the statement "every planar graph has a vertex with degree less than or…

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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: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: Consider a graph G which is a complete bipartite graph. The graph G is defined as K(3,4), meaning it…

A: A complete bipartite graph K(m,n) has two sets of vertices, with m vertices in one set and n…

Q: shortest path to any other vertex?

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Q: The graph G is a planar connected graph. It has 26 edges, and 19 vertices. How many faces does G…

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

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