1. Draw a simple graph with six vertices such that each vertex has degree three. How about drawing with only five vertices (each with degree three)?

Q: 1. In a complete graph with 5 vertices, how many triangles are there? (Remember: a triangle has 3…

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Q: What is the chromatic number of the graph K33, the graph with 33 vertices each connected to each…

A: We have graph K33 with 33 vertices connected to each other. So, we have a complete graph K33

Q: 3. Either draw a graph with the specified properties or explain why no such graph exists. a. Graph…

A: Given problem is :

Q: Need help with this question. Please explain each step and neatly type up. Thank you :)

A: Here are five different trees, each with a maximum degree of 3 and at least five vertices. For each…

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: . Consider a connected graph on 100 vertices with 99 edges. What's the mallest number of colors you…

A: If there is a connected graph with n vertex and n-1 edges then graph must be a path P(n).  Every…

Q: How many edges does this graph have?

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Q: 10) Add one edge to the graph in order to get a regular graph of degree 3.

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Q: 23. If a planar drawing of a graph has 15 edges and 8 vertices, how many faces does the graph have?

A: Answer :- We know from the Euler formula that  v+f =e+2

Q: a bc b a c a bd e d ce e

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Q: What is the smallest number of colors you need to properly color the vertices of K3.3 ? That is,…

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Q: 2) We have the graph C7 a) Determines the number of edges the graph has C7. b) Draw a graph C7.

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Q: Test on Euler and Hamilton Paths and Circuits. Questions and Answers 1. List the vertices in the…

A: Vertex is where two or more edges meet. The degree of a vertex is the number of edges originating…

Q: b) An undirected graph is n-regular if all vertices have degree n. For example, the graphs below are…

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Q: 1) Find the degree of each vertex in the following graph

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Q: B D С A F E G

A: 1. for a trail or circuit to be a Euler trail or circuit. An undirected graph has an Euler trail if…

Q: 11. Can the following graph be properly coloured?

A: Step 1:We must examine the vertices and their connections to ascertain whether the graph may be…

Q: Could there be a graph with four vertices of degree 1,2,5 and 4? Explain why no such graph exists or…

A: To verify whether a graph with 4 vertices of degree 1,2,5 and 4 exist or not.

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: A simple connected graph with 2,024 vertices is such that there are exactly two vertices, u and v,…

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Q: If a planar graph has 18 vertices and 26 edges, how many regions are determined when you draw t…

A: We have to solve given problem: